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  8448   Fri Apr 12 10:33:42 2013 CharlesSummaryISSDC-Coupled ISS Servo Design

General ISS Design

Signals through the ISS are directed as follows:  an error signal is obtained by summing the ~5 V signal from the PD with a -5 V signal from a high precision voltage regulator (which is first filtered with an ~ 30 mHz low-pass Sallen-Key filter).  It is this signal that is processed/amplified by the servo. The output from the servo is then used to drive an AOM (it is not known exactly how this is done and whether or not any preamplifier/extra circuitry is necessary). The resulting modulation, hopefully, reduces fluctuations in the laser intensity incident on the PD, lowering the relative intensity noise.

Servo Design

Almost the entirety of my focus has been directed toward designing the servo portion of the ISS. Speaking in general terms, the currently proposed design consists of stages of active op-amp filters, but now the stages will have internal switches that allow them to switch between ‘flat’ gain buffers and more complicated filters with our desired behavior. Consider some Example Filter Stages where I have demonstrated a typical switching filter with the switch open and closed. When the switch is closed, the capacitor is shorted and we simply have a variable gain buffer (variable in the sense that its gain can be tuned by proper choice of the resistances) with no frequency dependence. When the switch is open, the capacitor introduces a pole at ~100 Hz and a zero at ~1 kHz.

CircuitLab has decent analysis capabilities and attached are plots generated by CircuitLab. The first plot corresponds to a frequency analysis of the voltage gain of op-amp U1 and the ‘flat’ ~20 dBV gain filter with the switch closed and the capacitor shorted. The second plot is the same frequency analysis, but now with op-amp U2 and the filter with the switch open and the capacitor introduced into signal processing. This particular combination of resistors and capacitors produce a DC gain of 60 dBV, a pole at ~100 Hz, a zero at ~10 kHz and high frequency behavior of ~constant gain of 20 dBV. In this simulation, the gain-bandwidth product of the simulated op-amp (the standard op-amp CircuitLab uses) was artificially increased in order to see more ideal behavior in the higher frequency domain.

Switches like the above can be used to add boosts to some initial filter state (which could be like the above or possibly a simple integrator to achieve high DC gain) and change it into a more complex and more useful filter state advantageous for desired noise suppression. Cascades of these switching filters could be used to create very complicated transfer function behavior. No general servo has yet been designed as the exact details of the intensity noise requirements are still being determined.

With regards to the implementation of the switches, some ‘smart’ signal will be used to trigger a switch opening and the boost being introduced to the signal processing. The switches will be opened (open corresponds to adding the boost) in a manner that maintains stability of the servo circuit. Essentially, some sort of time delay or power monitor induced signal (power from the PD output) will be used to modify the servo's behavior.

AOM

How exactly the signal will drive the AOM for correct noise suppression is unknown currently.

 

Attachment 1: Example_Switching_Filter_Transfer_Function_-_Switch_Closed.png
Example_Switching_Filter_Transfer_Function_-_Switch_Closed.png
Attachment 2: Example_Switching_Filter_Transfer_Function_-_Switch_Open.png
Example_Switching_Filter_Transfer_Function_-_Switch_Open.png
  8474   Mon Apr 22 20:17:05 2013 CharlesUpdateISSNew Servo w/switching filters

 

In my previous post here, a new servo design was discussed. Although the exact design used will depend on the particular noise requirements for the 40m and the Bridge Labs (requirements will be considered separately for each application), I still have to yet to see those formalized. Despite this, I have been simulating an example servo circuit with three switchable stages. The design can be found at: New Servo.

Essentially, this circuit consists of three unity gain buffers that can be switched into different filtering states. Attached is a plot of the transfer function of this particular circuit with successive stages turned on. The curve (0) corresponds to all of the filters being switched off, so the total behavior is that of a unity gain buffer. The curve (1) corresponds to the first stage being turned on with the 2nd and 3rd still acting as unity gain buffers. This first state has a gain of ~80 dB at DC and a pole at ~10 Hz which sets the unity gain crossing at ~100 kHz. The curves (2) and (3) correspond to the second and third stage being turned on, respectively. Each of these stages has a pole at DC (i.e. ~infinite gain) and a zero at 10^4 Hz. For f > 10^4 Hz, these stages have gain ~ 1, as we can see in the transfer function below.

I have also performed some noise analysis of this circuit. Attached are a few plots produced by LISO showing the resistor and op-amp noise separately (it was too cluttered on one plot) at the output node of the servo. Both of these plots have a "Sum Noise" trace, which is the sum for every circuit element and is thus identical between plots. The third noise spectrum included is simply the noise at the output referenced to the input with the previously computed transfer function. I'm not sure if there is a simple method embedded in LISO to reference the noise at the output node to the input, but it should be as simple as numerically dividing the noise spectrum by the transfer function between input and output. 

Next, I will be attempting time-dependent simulations of this simple circuit using delayed switches instead of manually controlled ones.

Attachment 1: Servo_v0.1.png
Servo_v0.1.png
Attachment 2: Example_Filter_-_Transfer_Function_(mag).png
Example_Filter_-_Transfer_Function_(mag).png
Attachment 3: Example_Filter_-_Transfer_Function_(phase_in_final_state_only).png
Example_Filter_-_Transfer_Function_(phase_in_final_state_only).png
Attachment 4: New_Servo_-_Op-Amp_Noise.jpg
New_Servo_-_Op-Amp_Noise.jpg
Attachment 5: New_Servo_-_Resistor_Noise.jpg
New_Servo_-_Resistor_Noise.jpg
Attachment 6: New_Servo_-_Total_Noise_Input-Referenced.png
New_Servo_-_Total_Noise_Input-Referenced.png
  8748   Tue Jun 25 22:57:01 2013 CharlesUpdateISSProposed ISS for CTN Experiment

Following Tara's noise budget, I have developed the following ISS, whose transfer function was computed with LISO and is also displayed below. The transfer function was computed from the output of the differential amplifier circuit (i.e. it does not include the portion of the schematic in the dashed box). The differential amplifier is included for completeness. Essentially, the resistor values of this portion (and even the voltage reference if need be) can be modified to handle various signals from PDs in different experiments. Some filtering may also be applied to the signal from the voltage reference. In previous designs for the ISS, a ~30 mHz low-pass filter applied to the output of the voltage reference has also been proposed.

Screen_Shot_2013-06-25_at_10.24.07_PM.png

TF_Mag-CTNServo_v2.png

LISO was also used to compute the input-referred noise of this circuit. Using the response function of Tara's PD the noise spectrum was converted from [V / sqrt(Hz)] to [W / sqrt(Hz)] and then subsequently converted to a frequency noise spectrum, specifically [W / sqrt(Hz)] to [Hz / sqrt(Hz)], using the following transfer function which couples RIN to frequency noise in the CTN experiment. In these particular units, we can make a direct comparison between the inherent noise contribution from the servo itself and other more significant noise contributions shown earlier in Tara's noise budget. Indeed, the servo contributes significantly less noise.

Input_Noise-Freq-CTNServo_v2.png

This servo has been prototyped on a breadboard and will soon be characterized with the SR785. Additionally, schematics will be drawn up in Altium and eventually put on PCB.

Additional servos for other experiments can be designed once various requirements for noise suppression are explicitly formalized.

  8759   Wed Jun 26 21:52:55 2013 CharlesUpdateISSCTN Servo Prototype Characterization

Following the circuit design in elog 8748, I constructed a prototype for the servo portion of the ISS (not including the differential amp) to be used in the CTN experiment. The device was built on a breadboard and its transfer function was measured with the Swept Sine measurement group of an SR785. For various excitation amplitudes, the transfer function (TF) was not consistent.

TF_Mag-CTNServo_v2_Prototype.png

Recall the ideal transfer function for this particular servo and consider the following comparisons.

  • The unity gain frequency is consistent, and the measured TFs all exhibit some amount of 1/f behavior up to this point, but there is no zero around f~10^3 and individual low-frequency poles/zeros are not visible.
  • For each of the inputs, there is a feature that is not exhibited in the ideal TF. We see a large drop in gain a little past 10^3 Hz for a 100mV input, just past 10^2 Hz for a 10 mV input and around 10^1 Hz for a 1 mV input.
  • The ideal TF also goes as 1/f for f < 10 Hz, so I believe the low-frequency behavior of each of the above transfer functions is simply a physical limitation of the breadboard or the SR785, although I don't think this is caused by the circuit elements themselves. I used OP27 op-amps in the prototype as opposed to AD829 op-amps which are must faster and end up amplifying noise. To ensure that these op-amps were not the source of the gain limitation, I also tried using AD829 op-amps. The resulting transfer functions are shown below.
  • Both the frequency at which we see the anomalous feature and the maximum gain increase nearly proportional to the increasing input excitation amplitude.

This gain limitation is problematic for characterizing prototypes as my particular servo has very large gain at low frequencies. 

TF_Mag-CTNServo_v2_Prototype_AD829s.png

At the risk of looking too deeply into the above data,

  • It appears there is a slight change in slope around f ~ 10^3 Hz which would be consistent with the ideal TF.
  • For f > 10^3 Hz, one can easily see the TF goes as 1/f. The slope for f < 10^3 Hz is not as clear, although it obviously does not show 1/f^2 behavior as we would expect from the ideal TF.
  • We see the same gain limitation around G ~ 55 as we did with OP27 op-amps.

Unfortunately, the noise was too large for lower excitation amplitudes to be used to any effect. I'll try this again tomorrow, just as a sanity check, but otherwise I will proceed with learning Altium and drawing up schematics for this servo.

 

  8771   Thu Jun 27 18:24:25 2013 CharlesUpdateISSCTN Servo Prototype Characterization - Done Correctly

As I showed in [elog 8759], measuring the transfer function of my prototype servo was difficult due to physical limitations of either some portion of the construction or even the SR785 itself. To get around this, I tried using lower input excitation amplitudes, but ran into problems with noise.

Finding a TF consistent with theoretical predictions made by LISO was easy enough when I simply measured the TF of each of the two filter stages individually and then multiplied them to obtain the TF for the full servo. I still noticed some amount of gain limitation for 100 mV and 10 mV inputs, although I only had to lower the input to 5 mV to avoid this and thus did not see significant amounts of noise as I did with a 1 mV input. The individual transfer functions for each stage are shown below. Note that the SR785 has an upper cutoff frequency of 100 kHz so I could analyze the TF beyond this frequency. Additionally, the limited Gain Bandwidth Product of OP27 op-amps (used in the prototype) causes the magnitude and phase to drop off for f > 10^5 Hz approximately. The actual servo will use AD829 op-amps which have a much larger GBWP.

TF-CTNServo_v2_Prototype-Individual_Stages.png

The measured TFs above are very close to ideal and agree quite well with theoretical predictions. Based on the [circuit schematics],

  • Stage 1 should have Gain ~ 10^3 until the pole at f ~ 10 Hz  
  • Stage 2 should exhibit a DC pole, a zero at f ~ 10^3 Hz and then unity gain for f > 10^3 Hz

Indeed, this is exactly what we can see from the above two TFs. We can also multiply the magnitudes and add the phases (full_phase = phase1 + phase2 - 180) to find the TF for the full servo and compare that to the ideal TF produced by LISO,

TF-CTNServo_v2_Prototype-Calc_vs_Meas.png

And we find exceptionally consistent transfer functions, which speaks to the functionality of my prototype 

As such, I'll proceed with designing this servo in Altium (most of which will be learning how to use the software)

Note that all TFs were taken using the netgpibdata python module. Measurement parameters were entered remotely using the TFSR785.py function (via control room computers) and following the examples on the 40m Wiki.

Attachment 3: TF-CTNServo_v2_Prototype-Individual_Stages.fig
Attachment 4: TF-CTNServo_v2_Prototype-Calc_vs_Meas.fig
  8786   Fri Jun 28 16:19:06 2013 CharlesUpdateISS40m Noise Budget - Seismic Contribution

 I'm working on developing a full noise budget for the 40m. To that end, I'll use measurements from the GUR1 seismometer to characterize seismic noise. Without any unit calibration, I found the following spectrum,

seismic_noise_6-28-13_raw.png

To extract useful information from this data, I first used the calibration from "/users/Templates/Seismic-Spectra_121213.xml" to obtain the spectrum in [m / s / sqrt(Hz)].

calibrated_data = raw_data * 3.8e-09

I then divided each point in the power spectrum by the frequency of said point to obtain [m / sqrt(Hz)]. I don't think we can simply divide the whole spectrum by 40 meters to obtain [RIN / sqrt(Hz)], although that was my immediate intuition. Having power spectra of all the major noise contributions in units of [RIN / sqrt(Hz)] would make designing an appropriate filtering servo fairly straightforward.

 seismic_noise_6-28-13_meters.png

 

Attachment 2: seismic_noise_6-28-13_raw.fig
Attachment 4: seismic_noise_6-28-13_meters.fig
  8791   Tue Jul 2 12:59:46 2013 CharlesUpdateISSGeneral Design for ISS Applicable to Multiple Applications

 While attempting to develop a somewhat accurate noise budget for the 40m, I reasoned that while the shape of the transfer function for the ISS is important, the degree to which we can 'tune' it to a particular experiment/application is limited.

  • Since we're using a DC-coupled servo, the TF magnitude will go like f^k with k < 0 for low frequency.
  • The UGF will be somewhere around 10 kHz to 1 MHz (most likely right around 100 kHz) as beyond 1 MHz, the gain of our servo is limited by the GBWP of the op-amps.
  • We need around 3 or 4 orders of magnitude of gain in the 1-100 Hz range based on this, with gain > 10 for f < 10 kHz

Beyond that, we're sort of limited by the desired high and low frequency behavior as well as the general principle that more electronics = more noise so we probably don't want more than 3 or 4 filter stages, if that. Additionally, the ISS can be over-engineered so that it suppresses the laser noise to levels well below other fundamental noise sources over the important regime ~10 - 10^3 Hz without particular regard to a noise budget.

The design I propose is very similar to a previous design, with a few adjustments. It consists of 3 filter stages that easily be modified to increase gain for higher frequencies if it is known/determined that the laser being stabilized has a lot of high frequency noise.

40mServo_v1.png

Stage 1: Basic LP Filter + Establish UGF (each stage 'turning on' will not change the UGF),  Stage 2: Integrator with zero @ 10 kHz,  Stage 3: Optional extra gain if necessary

40mServo_v1-Stage1.pdf40mServo_v1-Stage2.pdf40mServo_v1-Stage3.pdf

With the full TF given by,

 40mServo_v1.pdf 

As usual we consider the noise caused by the servo itself. Noise analysis in LISO is done with a 1 V input excitation.

40mServo_v1-Input_Noise.pdf

This servo should function sufficiently for the 40m.

  8799   Wed Jul 3 20:51:43 2013 CharlesUpdateISSProposed ISS for CTN Experiment - Altium Schematic

 After familiarizing myself with Altium, I drew up the attached schematic for the ISS to be used in the CTN experiment. The filename includes 'abbott-switch' as I am using an Altium component (the switch, in particular), that he created. The MAX333A actually has 20 pins on a single component, but the distributed component that he created is useful for drawing uncluttered schematics. I won't be using all of the pins on this switch, but for completeness, I have included the 3rd and 4th portion of the full component in the upper right hand corner.

Currently, the schematic includes the voltage reference (AD586), a LP filter for the reference signal, the differential amplifier stage to obtain the error signal and then finally all of the filter stages. The schematic does not include the RMS detection and subsequent triggering of each filter stage. The TRIGGER 1 signal is a user input (essentially the on button) while the TRIGGER 2 signal will flip the second switch when the RMS noise has decreased sufficiently after the first filter stage has been turned on. 

PCB layouts will be done once I understand that part of Altium 

 

NOTE THAT I HAVE DELETED ELOG 8798 AS IT WAS A DUPLICATE OF THIS ONE.

I wanted this elog to be in reply to a previous one and I couldn't figure out how to change that in an elog I already submitted.

 

 

 

Attachment 1: CTNServo_v2_abbott-switch.pdf
CTNServo_v2_abbott-switch.pdf
  8830   Thu Jul 11 13:52:51 2013 CharlesUpdateISSRMS threshold detection and triggering

There are essentially two major portions of the ISS I am designing. One system has the voltage reference, differential amplifier and filtering servo (schematic attached) while the other has a comparator circuit and a triggering mechanism. The first system amplifies an error signal obtained from the PD output and the voltage reference, which is then fed back through the AOM. I've done a lot of work designing/prototyping this first half and now I'm starting to design the second half.

The second system's main purpose is to maintain loop stability as the ISS is engaged. Let's assume a user has decided they want noise suppression. They would first close the ISS feedback loop and an error signal would pass through three unity-gain buffers, providing minimal noise reduction. The user can then send a signal to theTRIGGER 1 port to switch the first stage from its unity-gain position to its filtering position and reduce the intensity noise further. This signal will most likely be digital in origin. Alternatively, when the user first closes the ISS loop, the first stage can already be in its filtering position rather than necessitating two commands.

A test channel (not drawn in the included schematic) will monitor the RMS level of the incoming signal from the PD. This noisy AC signal will first be amplified and then passed through an RMS-to-DC converter. The resulting DC signal is used as a part of the triggering mechanism for later stages. Once the first stage has been switched manually, and the DC signal corresponding to RMS noise of the PD output drops below a certain threshold, stages 2 and 3 will be internally triggered with a short delay between them. Toward being able to detect this threshold, I have designed a simple comparator circuit with an LT1016. The circuit has a fairly low-level output when the input voltage is larger than the threshold (about 1.6 V for my simple prototype), but when the input passes below the threshold, the comparator puts out almost 4 V, a number limited by the supply voltage. The schematic is shown below.

Simple_Comparator_Circuit.png

The component V2 and the various voltage dividers serve to establish the reference/threshold voltage. Note that although the LT1016 is not powered in the schematic, it requires ±5 V (a max of 7 V). The above circuit was also prototyped on a breadboard and I characterized it with an oscilloscope. Using a CFG253, I made a low frequency (~0.3 Hz) triangle wave with an amplitude and DC offset such that it oscillates between 0 and 5 V. This was applied to the IN node in the above schematic. The input waveform and the circuit's response (voltage at the OUT node) are shown below. As expected, R2 serves to establish hysteresis. The comparator switches to 'high' output until the input drops below 1.6 V, and then it doesn't switch back to the 'low' output until the input goes up to ~3.4 V.

F0001TEK.JPG

This behavior is ideal for our application as we can detect when the DC signal from the RMS-to-DC converter drops below a certain level (i.e. the first stage that has been activated does some amount of filtering to lower RMS noise), and then we can trigger subsequent filter stages off of the comparators high-level output. 

This circuit could easily be used to drive the MAX333a switches shown in the first schematic attached. I believe the low-level output is not sufficient to switch the MAX333a although the ~4 V high-level output is quite sufficient. Regardless, these exact values (thresholds, outputs etc) will be determined after I have a better idea of the RMS noise of the laser without any intensity stabilization as well as a solid understanding of how the AD8436 RMS-to-DC converter works. This was simply a proof of concept for lower threshold detection using basic Schmitt trigger topology.

Attachment 1: 40mServo_v1.pdf
40mServo_v1.pdf
  8836   Fri Jul 12 12:51:13 2013 CharlesUpdateISSRMS Noise from PMC Transmission

I went out on the floor to look at the transmitted signal from the PMC to get a rough idea of the noise of the unstabilized laser. There was already a scope hooked up so I just used the measurement features to find the following:

Signal average = 875 mV.  Peak-to-Peak noise = 45 mV

Assuming the noise can be approximated as Gaussian noise, the heuristic for converting to RMS noise of the signal is RMS = Peak-to-Peak / 8 (or Peak-to-Peak / 6, I've used both...)

-> RMS Noise ~ 6.5 mV

When designing my filtering stages and RMS detection/triggering, I'll use relative RMS, i.e. 6 mV / 875 mV = 0.007, as a measure of unstabilized laser noise.

  8839   Fri Jul 12 18:30:20 2013 CharlesUpdateISSRMS Noise from PMC Transmission

Quote:

It would be better to measure the power spectrum density of the fluctuation.
The RMS does not tell enough information how the servo should be.
In deed, the power spctrum density gives you how much the RMS is in the entire or a specific frequency range.

I wanted the RMS noise simply to establish a very rough estimate of thresholds on RMS detectors that will be part of my device. If you refer to elog 8830, I explain it there. Essentially, when the ISS is first engaged, only one of the 2 or 3 filter stages will be active. Internal RMS threshold detection serves to create a logic input to switch subsequent filters to their 'on' stage.

  8876   Thu Jul 18 21:45:36 2013 CharlesUpdateISSISS - Full Schematic

 Here I have included the full schematic (so far) of the proposed ISS. There are two sheets: the first schematic details the filter stages and their accompanying circuitry while the second schematic details the RMS threshold detection and subsequent triggering.

The first schematic is fairly self explanatory as to what different portions do, and I have annotated much of the second schematic as there are some non-traditional components etc.

I have not yet included some mechanism to adjust the threshold voltage in real time or any of the power regulation, but these should follow fairly quickly.

Attachment 1: 40mServo_v1.pdf
40mServo_v1.pdf 40mServo_v1.pdf
  8920   Wed Jul 24 22:58:03 2013 CharlesUpdateISSISS - Full Schematic - Updated

 I have made significant changes to the ISS schematic, mostly in the form of adding necessary subsystems.

Some changes I have made:

  • Added a front page with sheet symbols that are representations of the other schematic sheets.
  • Added an 'Excitation' subsystem for use in determining the closed-loop transfer function
  • Added an instrumentation amplifier (with ADA4004s at Rana's recent suggestion) to handle the differential input from the PD
  • Included a switchable inverting amplifier (Gain of 1 or -1) to ensure we have the correct polarity
  • Made it so the first filtering stage is immediately active when the ISS loop is closed
  • Added LP filters with large time constants to buffer/delay trigger signals
  • Added test points all over the board
  • Refined a few buffer amplifiers

On the front page, all inputs and outputs are currently BNC ports, although this is most likely not the final design that will be used. For instance, the ports ENABLE, INPUT GND and INVERT are supposed to be logic inputs for a MAX333a switch. These will most likely be front panel switches that either connect the switch's logic pin to GND (Logic 0) or something like a +5 V supply (Logic 1).

I also have not included power regulation for my board although I have some of the actual D1000217 Chasis Power Regulator boards and I'll incorporate those in my design soon.

Attachment 1: 40mServo_v1.pdf
40mServo_v1.pdf 40mServo_v1.pdf 40mServo_v1.pdf 40mServo_v1.pdf 40mServo_v1.pdf
  8922   Thu Jul 25 12:53:45 2013 CharlesUpdateISSComparator + Triggering Prototype

 I realized I totally forgot to post this last week, but I prototyped the comparator and boost triggering portion of the ISS, at least in part. Below is a schematic that shows the prototype circuit I made. Note that it includes ports for the oscilloscope channels that appear in the second image included. Essentially, I was able to verify that the output from the LT1016, as it's currently constructed in the ISS schematic, would be sufficient logic to switch the MAX333a.

Comparator_Prototype.png

Below, we can first see that the comparator is switching its output as desired. When the DC level of the input drops below a certain threshold (~1.6 V) the output of the comparator switches on to ~4 V. When the DC level of the input goes back up above the upper threshold (~3.2 V), the comparator switches off to ~0.3 V. The exact values of the threshold voltages can be determined/tuned at a later date, but this is the basic behavior that the comparator circuit will have.

To detect whether or not the MAX333a was switching properly, I connected the common terminal of one of the switches to a +5 V supply, and looked at the voltage coming off both the 'open' and 'closed' terminals of said SPDT switch. We can see that with Logic 0 (comparator output ~0.3 V) Channel 4 exhibits a ~5 V signal, just as we would expect from the above schematic. With Logic 1 (comparator output ~4 V), Channel 3 exhibits the characteristic 5 V signal.

Comp_Triggering_Behavior.jpg

  8927   Fri Jul 26 14:39:08 2013 CharlesUpdateISSPower Regulation for ISS Board

I constructed a regulator board that can take ±24 V and supply a regulated ±15 V or ±5 V. I followed the schematics from LIGO-D1000217-v1.

I was going to make 2 boards, one for ±15 V and one for ±5, but Chub just gave me a second assembled board when I asked him for the parts to construct it 

 

  8928   Fri Jul 26 22:19:24 2013 CharlesUpdateISSISS - Full Schematic - Updated

Quote:

 I have made significant changes to the ISS schematic, mostly in the form of adding necessary subsystems.

Some changes I have made:

  • Added a front page with sheet symbols that are representations of the other schematic sheets.
  • Added an 'Excitation' subsystem for use in determining the closed-loop transfer function
  • Added an instrumentation amplifier (with ADA4004s at Rana's recent suggestion) to handle the differential input from the PD
  • Included a switchable inverting amplifier (Gain of 1 or -1) to ensure we have the correct polarity
  • Made it so the first filtering stage is immediately active when the ISS loop is closed
  • Added LP filters with large time constants to buffer/delay trigger signals
  • Added test points all over the board
  • Refined a few buffer amplifiers

On the front page, all inputs and outputs are currently BNC ports, although this is most likely not the final design that will be used. For instance, the ports ENABLE, INPUT GND and INVERT are supposed to be logic inputs for a MAX333a switch. These will most likely be front panel switches that either connect the switch's logic pin to GND (Logic 0) or something like a +5 V supply (Logic 1).

I also have not included power regulation for my board although I have some of the actual D1000217 Chasis Power Regulator boards and I'll incorporate those in my design soon.

 More changes that I've made:

  • Added daughter boards for power regulation. Currently I have ±24V going into two boards, with ±15V coming out of one and ±5V coming out of the other. Again, these are based off of LIGO-D1000217
  • Added an optional Dewhitening filter (with p=1Hz and z=100Hz, although these can easily be changed) to accommodate any PD's that have whitening
  • Added a bypass to allow the boosts (stages 2 and 3 of the filtering servo) to be enabled/disabled by a front panel switch
  • I also put in jumpers that can be used to provide Logic 1 (boost enabled) to both Boost 1 and Boost 2 without depending on the internal RMS detection/triggering
  • Changed the input grounding switch so that it's set up correctly. Before, it was taking the PD signal and sending it to GND, not actually grounding the input to the rest of the ISS 
Attachment 1: 40mServo_v1.pdf
40mServo_v1.pdf 40mServo_v1.pdf 40mServo_v1.pdf 40mServo_v1.pdf 40mServo_v1.pdf
  8959   Thu Aug 1 22:58:45 2013 CharlesUpdateISSCTN Servo - Explicit Requirement and Proposed Servo

 In PSL elog 1270, Evan elucidated the explicit requirements for the CTN ISS board. Essentially, the transfer function of the ISS should be something like:

     TF_mag = (Unstabilized RIN) / (Calculated RIN Requirement)

I took Evan's data and did exactly this. I then designed a servo (using the general design I proposed here) to meet this requirement with a safety factor of ~10. By safety factor, I mean that if the ISS operates exactly according to theory, it should suppress the noise by a factor of 10 more than what is necessary/set out by the requirement. Below is a plot of the loop gain obtained directly from the requirement (the above expression for TF_mag) and the transfer function of the servo I am proposing.

CTN_Servo_TF_-_Proposed_v_Req.png

I don't have the actual schematics attached as I was working with a LISO file and have yet to update the corresponding Altium schematic. The LISO file is attached and I will add the schematics later, although one can reference the second link to find a simple drawing.

Attachment 2: CTNServo_v3.fil
# Stage 1
r R31 1.58k in n_inU3
op U3 ad829 p_inU3 n_inU3 outU3
r R35 1k p_inU3 gnd
c C33 1u p_inU3 gnd
c C32 10n n_inU3 outU3
r R34 158k n_inU3 outU3

# Stage 2
#r R41 15.8 outU3 n_inU4U5
... 24 more lines ...
  8961   Fri Aug 2 21:59:36 2013 CharlesUpdateISSFinalized ISS Schematic (hopefully)

Attached is the finalized schematic. The general circuit topology should remain the same from this point forward, although individual component values are subject to change. I will also be adding some more annotations to ensure everything on the board is clear.

In general, I have finally included all of the correct components (i.e. front panel switches are now actually switches and front panel LEDs are now included). I also added an external 'Boost' switch, which can be used to enable or disable the boosts. The motivation for including this switch is that one might want to test functionality of the ISS without using the 'fancy' RMS detection and triggering circuitry. Additionally, one can disable the boosts when all the circuitry is stuffed in order to troubleshoot, so it essentially grants the board some flexibility in its operation.

I am now working on the PCB layout and I should hopefully have that done next week. 

Attachment 1: ISS_v3.pdf
ISS_v3.pdf ISS_v3.pdf ISS_v3.pdf ISS_v3.pdf ISS_v3.pdf
Attachment 2: ISS_v3-Power_Reg.pdf
ISS_v3-Power_Reg.pdf
  9016   Thu Aug 15 21:42:53 2013 CharlesUpdateISSISS - Schematic + PCB Layout

 After many, many moons of getting to know exactly how frustrating Altium can be, I have completed the PCB layout for my ISS board (final page of ISS_v3.pdf).

Before I get into detail about the PCB, there is one significant schematic change to note: the comparator circuit was changed (with significant help from Koji) so that the voltage reference for boost triggering is established in a more logical way. Instead of the somewhat convoluted topology I had before, now there are only two feedback resistors, R82 and R83. Because their resistances (500k and 50k respectively) are so much larger than the total resistance of the 1k potentiometer (used to establish a tunable threshold voltage), the current flowing through the feedback loop is negligible compared to the 5 mA current flowing through the potentiometer (the pot is rated for 2 W and with 5 mA -> 25 mW dissapation). This allows one to set the threshold voltage for my schmitt trigger, at pin 2 of both the pot and the comparator, entirely with the pot. This trigger also has hysteresis given by the relation deltaV ~ (R83/R82) * (Voh - Vol) where deltaV is the separation between threshold voltages, Voh is the high-level comparator ouput and Vol is the low-level comparator output. Koji simulated this using CircuitLab and I plan to verify the behavior by making a quick prototype circuit.

Now, on to the PCB. The board itself is of a 'standard' LIGO size (11" x 6") has 3 routing layers and 3 internal planes, one for +15 V, one for -15 V and one for GND. In the attached pdf, red is the top routing layer, blue is the bottom layer and brown is the middle routing layer (used for ±5 V exclusively). The grey circles are pads and vias (drilled through) and anything in black is silkscreen overlay. I placed each component and track by hand, attempting to minimize the signal path and following the general rules below,

  • Headers for power, ±5 V and ±15V, are at the back of the board
  • For sections of the board such as filter stages or buffers, resistors and capacitors were grouped around their respective op-amps.
  • As often as was possible, routing was confined to the top layer. Tracks on the bottom layer were placed mostly out of necessity (i.e. no possible connection on top routing layer).
  • The signal generally proceeds from left to right (directions with respect to the attached printout) in the same logical order as on the schematic sheets. Refer to the global sheet (page 1) of the attached "ISS_v3.pdf".
  • External ports such as the PD input, various monitoring ports and panel mounted switches/LEDs were all connected to the board via headers located along the front edge. These are also ordered following the schematic layout.
  • Occasionally, similar signal paths were grouped together although this was a rarity on my board

Sections of the board have been partitioned and labeled with silkscreen overlay to help in both signal pathway recognition as well as eventual troubleshooting.

On the board, I have also included holes so that it can be mounted inside of an enclosure. There is a DCC number printed as well as a 'barcode' (TrueType font: IDAutomationC39S), although they both contain filler asterisks as I haven't published this to the DCC and thus do not have a number.

Attachment 1: ISS_v3.pdf
ISS_v3.pdf ISS_v3.pdf ISS_v3.pdf ISS_v3.pdf ISS_v3.pdf ISS_v3.pdf
Attachment 2: ISS_v3-Power_Reg.pdf
ISS_v3-Power_Reg.pdf
  9019   Fri Aug 16 19:36:49 2013 CharlesUpdatePSLPMC_trans Channel

Rana and I connected the PMC_trans output to the BNC connector board on the west end of the PSL table (the channel is labeled). I took a few spectra off of PMC_trans and the SR785 was connected directly to the PMC_trans output for about an hour.

Data will follow.

  9330   Sat Nov 2 19:36:15 2013 CharlesUpdateGeneralPossible misalignment?

 I was working on the electronics bench and what sounded like a huge truck rolled by outside. I didn't notice anything until now, but It looks like something became misaligned when the truck passed by (~6:45-6:50 pm). I can hear a lot of noise coming out of the control room speakers and pretty much all of the IOO plots on the wall have sharp discontinuities.

I haven't been moving around much for the past 2 hours so I don't think it was me, but I thought it was worth noting.

  9331   Sat Nov 2 22:49:44 2013 CharlesUpdateISSCTN ISS Noise Suppression Requirement - Updated 10/27

 Previously in elog 8959, I gave a very simple method for determining the noise suppression behavior of the ISS. Recently, I recalculated this requirement in a more correct fashion and again redesigned the ISS to be used in the CTN experiment.

  • Determining the Requirement

Just as before, the data from PSL elog 1270 is necessary to infer a noise suppression requirement. The data presented there by Evan consists of two noise spectra, 1) the unstabilized RIN presently observed in the CTN experiment readout and 2) the theoretical brownian noise produced by thermal processes in the mirror coating+substrate. The statement "TF_mag = (Unstabilized RIN) / (Calculated Brownian Noise Limit)", where TF_mag refers to the required open-loop gain of the ISS, is actually a first order approximation of the 'required' noise suppression. In fact if we wanted the laser noise to be suppressed below the calculated brownian noise level, it is more correct to say 

        Closed-loop ISS gain = (Calculated Brownian Noise Limit) / (Unstabilized RIN)

As this essentially gives a noise suppression spectrum i.e. a closed-loop gain in linear control theory. Below is a very simple block diagram showing how the ISS fits into the CTN experiment. The F(f) block represents my full servo board.

    ISS_path.png

Some of the relevant quantities involved:

            plant-quant_1.png

            plant-quant_2.png

So looking at the block diagram, our full closed-loop transfer function is given by,

cl-loop.png

So then to determine the required F(f), i.e. the required transfer function for my servo, we consider the expression 

               requirement.png

The plant transfer function is simply Plant = (C(f) * a * P * A) ~ 0.014 V/V, where I have ignored the cavity pole around 97 kHz as our open-loop transfer function ends up crossing unity gain around 10 kHz. In the above, I have included what I call a 'safety factor' of 10. Essentially, I want to design my servo such that it suppresses noise well beyond what is actually required so that we can be sure noise contributions to experiment readouts are not significantly influenced by the laser intensity noise.

  • Proposed Servo Design

Using the data Evan reported for the brownian noise and free-running RIN, I came up with an F(f) to the meet the requirement as shown below.

CTN_TF_req-vs-proposed.png

 Where the blue curve includes the safety factor mentioned before. This plot just demonstrates that using my modular ISS design, I can meet the given noise suppression requirements.

To be complete, I'll say a little more about the final design.  As usual, the servo consists of three stages. The first is the usual LP filter that is always 'on' when the ISS loop is closed. The boosts I have chosen to use consist of an integrator with a single zero and a filter that looks somewhat like a de-whitening filter. The simulated open-loop transfer functions are shown below.

switching-filters.png

 

 

 

 

 

 

 

 

  9332   Sun Nov 3 00:05:52 2013 CharlesSummaryISSISS Update - Bout' time

Right near the end of summer, I had an ISS board that was nominally working, but had a few problems I couldn't really sort out. Since I've been back, I've spent a lot of time just replacing parts, trying different circuit topologies and generally attempting to make the board function as I hoped it might in all those design stages. Below is a brief list of some of the problems I've been fixing as well as the first good characterization of the board transfer function that I've been able to get.

We'll start with some of the simple problems and proceed to more complicated ones.

  • The 5V reference I was using to obtain an error signal from some arbitrary DC photodiode readout was only producing ~2.5 V. 
    • Turns out I just need a FET type op-amp for the Sallen-Key Filter that I was using to clean up any noise in the reference output, as the leakage current in a AD829 was causing a significant voltage drop. I put in an OPA140 and everything worked marvelously.
  • The way I set up input grounding (i.e. send a ~0 amplitude signal through the board as an input) passed a few Amps through one of my chips causing it to burn out rather fantastically.
    • There isn't a good way to fix this on the current board (besides just getting rid of the functionality altogether) so my solution so far has just been to redesign that particular sub-system/feature and when we implement the second version of the ISS, the input grounding will be done correctly
  • One of the ICs I'm using, specifically the AD8436 RMS-to-DC converter, causes some super strange oscillations in -5V power line. When this chip is soldered onto the board, the -5V supply jumps between -3V and -10V rather sporadically and the DC power-supply used to provide that -5V says that board is drawing ~600 mA on that particular power line.
    • To date, I don't really have any idea what's going with this chip, and I've tried a lot of things to remedy the problem. My first thought was that I had some sort of short somewhere so I took the chip off the board, cleaned up all the excess solder and flux around the chip's footprint and then meticulously soldered a new chip on (when I say meticulously, it took over an hour to solder 20 little feet. I really really didn't want to short anything accidentally as the chip only comes in a package with ridicously small spacing between the leads). Lo and behold, nothing happened. I still saw the same oscillations in power supply and the board was still drawing between >500 mA on that line. Just to be sure, I soldered on a third chip taking the same amount of care and had the same problems.
    • I went over the schematic in Altium that we used to order the board, and unless the manufacturer made a mistake somewhere, there aren't any incorrectly routed signals would cause, say, two active devices to try setting the voltage of a particular node to different values.
    • I got some QSOP-to-DIP package converters so that I could mess around with the AD8436 on a breadboard to make sure it functioned correctly. I set up an identical circuit to the one on the PCB and didn't see any oscillations in the power supply, both for +-5V and +-15V as the chip can handle both supply voltages. I'm not really sure how to interpret this...
    • I'm still actively trying to figure this particular problem out, but I'm shooting in the dark at this point. 
  • Initial attempts to measure the transfer-function of the board were wrought with failure.
    • I figured out, with Nic's help, that the board needs the 'loop closed' with a significant broadband attenuator (to simulate the plant optics discussed in elog 9331) in order to not have constant railing of the high gain op-amp filter stages. Even after I did this, the measured transfer functions were not at all consistent with simulation. I wasn't sure if it was just a part issue, a design issue or a misunderstanding/bad data collection on my part so I just redesigned the whole servo and stuffed the board with entirely new components from around the 40m. Turns out the newly designed servo behaved more properly, as I will show below.

The above list encompasses all the issues I've had in making the ISS board function correctly. No other major problems exist to my knowledge.

I was able to measure both the open- and closed-loop transfer functions of the servo with the SR785. The results are shown below.

full-op-loop.png

The transfer function with the boosts on caps at a particular value set by op-amp railing, i.e. below 100 Hz, the op-amps are already putting out their max voltage. This is the usual physical limitation when measuring the transfer function of an integrator. We can also see that the measured phase follows the simulated phase above ~300 Hz. The 'phase matching' at low frequency is again do to the op-amp railing in the servo output..

The closed-loop gain is shown below,

full-cl-loop.png

The measured closed-loop gain with the boosts on again matches the LISO simulation quite well except at low frequency where we are limited by op-amp railing. We compare the measured closed-loop transfer function to the desired noise suppression stipulated in my previous elog 9331,

req-vs-meas.png

 And we might hopefully conclude that my servo functions as desired. One should note that the op-amp railing seen in these measurements is not indicative of limitations we might face in some application of the ISS for the following reason. These transfer functions were measured with a 100 mV excitation signal (it is necessary to keep this signal amplitude large enough so that the inherent signal-to-noise ratio of the excitation source is large enough for accurate measurement) which leads to somewhat prompt railing of the op-amps. When the ISS operates to actually stabilize a laser, the input error signal will be much smaller (on the order of a few 10's of mV or less) and will decrease significantly assuming correct operation of the ISS. This means we won't see the same type of gain limitations.

 

What now, you ask?

Aside from the problem with the AD8436 chip, the ISS board seems to be functioning correctly. The transfer functions we have measured are correct to within the component tolerances and all of the various subsystems are behaving as they were designed to. Moving toward the goal of having this system work in situ for the CTN experiment, I need to do the following things,

  • Design a housing for the board -> order said housing and the front panel previously designed
  • Make sure the power supply daughter PCB boards are compatible with the ISS board and can provide power correctly
  • Talk to Evan and Tara about integrating the ISS with their experiment and make sure my board can do everything it needs to in that context.

So close, or so I say all the time 

 

  9746   Mon Mar 24 19:42:12 2014 CharlesFrogsVACPower Failure

 The 40m experienced a building-wide power failure for ~30 seconds at ~7:38 pm today.

Thought that might be important...

  11124   Mon Mar 9 16:50:35 2015 Champagne DuckFrogsTreasureCelebrating Lock

Attachment 1: 2015-03-09_16.35.47.jpg
2015-03-09_16.35.47.jpg
  437   Tue Apr 22 17:08:04 2008 CarynUpdateIOOno signal for C1:IOO-MC_L
C1:IOO-MC_L signal was at zero for the past few days
  480   Thu May 15 14:39:33 2008 CarynSummaryPEMfiltering mode cleaner with mic
Tried filtering for mode cleaner data(C1:IOO-MC_L) using a siso-firwiener filter and microphone data(C1:PEM-AS_MIC) for noise input. The noise reduction in mode cleaner data using the microphone-filter is comparable to the noise reduction when an accelerometer(C1:PEM-ACC_MC1_X) filter is used. See attached graphs.
Attachment 1: MC_L_with_PEM-AS_MIC_filter.pdf
MC_L_with_PEM-AS_MIC_filter.pdf
Attachment 2: MC_L_with_PEM-ACC_MC1_X_filter.pdf
MC_L_with_PEM-ACC_MC1_X_filter.pdf
  494   Fri May 23 21:21:52 2008 CarynSummaryGeneralfiltering mode cleaner with wiener filter
I tried filtering some saved MC_L data (from Mon May19 4:30pm) with multiple MISO filters of different orders, with various sampling rates, at different times. Plotted the max rms error (where error is signal minus signal-estimate). 2min of data (around Mon May19 4:30pm) were used to calculate each filter. And each filter was applied to data at later times to see how well it performed as time progressed. Plots are attached. There appears to have been a disturbance during the 3rd hour. Rana pointed out perhaps it would be better to use data from the evening rather than during the day.
Attachment 1: error_vs_N_for_different_times_64Hz.pdf
error_vs_N_for_different_times_64Hz.pdf
Attachment 2: error_vs_N_for_different_times_128Hz.pdf
error_vs_N_for_different_times_128Hz.pdf
Attachment 3: error_vs_N_for_different_times_256Hz.pdf
error_vs_N_for_different_times_256Hz.pdf
Attachment 4: error_vs_N_for_different_times_512Hz.pdf
error_vs_N_for_different_times_512Hz.pdf
Attachment 5: error_vs_srate_for_different_times_256.pdf
error_vs_srate_for_different_times_256.pdf
Attachment 6: error_vs_srate_for_different_times_512.pdf
error_vs_srate_for_different_times_512.pdf
Attachment 7: error_vs_srate_for_different_times_1024.pdf
error_vs_srate_for_different_times_1024.pdf
Attachment 8: error_vs_time_for_different_srates_256.pdf
error_vs_time_for_different_srates_256.pdf
Attachment 9: error_vs_time_for_different_srates_512.pdf
error_vs_time_for_different_srates_512.pdf
Attachment 10: error_vs_time_for_different_srates_1024.pdf
error_vs_time_for_different_srates_1024.pdf
  518   Wed Jun 4 16:25:06 2008 CarynSummaryPEMmicrophone moved
The microphone 'C1:PEM-AS_MIC' has been moved right a bit. This change didn't seem to have much effect on filtering the 'C1:IOO-MC_L' signal, at least not compared to how the filter changes with time. Also used microphone data to filter MC_L data using firwiener filter/levinson. The N(order) and sample rate were varied to see how the filter changed. Attached are graphs of the max(rms(noise_estimate)) vs N or IR for varying srate. Note that filtered_signal=signal-noise_estimate. So, the larger the noise_estimate, the more the filter subtracts from the signal.
Green-filtered signal
blue-noise estimate
red-MC_L signal
note decreasing sample rate is more effective than increasing N (higher N takes more time to compute)
note sample rate doesn't change the max(rms(noise_estimate)) very much if impulse response time remains constant
note the 64hz, N=7000 (impulse response about 110s) filter is a better filter than the 512Hz, N=7000(impulse response about 14s)
Attachment 1: 1_MC_L.pdf
1_MC_L.pdf 1_MC_L.pdf 1_MC_L.pdf 1_MC_L.pdf
  522   Fri Jun 6 11:19:13 2008 CarynSummaryPEMFiltering MC_L and MC_F with PEM:ACC and microphone
Tried to filter MC_L and MC_F with acc/seis data and microphone data using wiener filter (levinson)

-Used get_mic_data.m and miso_filter_lev.m to make SISO filter for 2 minutes of IOO-MC_F data. Used PEM-AS_MIC signal as noise input data. Filters calculated at initial time were applied to later data in 1 hour intervals.
-microphone filter did not seem to filter MC_F very well in high frequency range using this filtering procedure.
-residual is larger than est (see MC_F pdf)
-Used do_all_time_lev.m to make graph of max(rms(residual)) to N(order) for different times.(note for each N, filter was calculated for initial time and then applied to data at other times).
-relation of max(rms(residual)) to N(order) is time sensitive (note-on graph, time interval is 1hour) (see MC_F pdf)
-Presumably, max(rms(residual)) should decrease as N increases and increase as time increases since the filter probably becomes worse with time. I think the reason this isn't always true in this case is that the max(rms(residual)) corresponds to a peak (possibly a 60Hz multiple) and the wiener filter isn't filtering out that peak very well.


-Used get_z_data.m and miso_filter_lev.m to make MISO filter for 2 minutes of IOO-MC_L used the following signals as noise input data
PEM-ACC_MC1_X
PEM-ACC_MC2_X
PEM-ACC_MC1_Y
PEM-ACC_MC2_Y
PEM-ACC_MC1_Z
PEM-ACC_MC2_Z
PEM-SEIS_MC1_Y
-Filter was applied to later data in 2hour intervals.
-Used do_all_time_lev.m to make graph of max(rms(residual)) to N(order) for different times.(note for each N, filter was calculated for initial time and then applied to data at other times).
-acc/seis filter seemed to filter MC_L OK for 128,256,512Hz srates. 64 Hz wasn't ok for certain N's after a period of time.
-residual is smaller than est for srates not 64Hz (see MC_L pdf)
-residual is larger than est for 64Hz at N=1448 for later times (see MC_L pdf)
-relation of max(rms(residual)) to N is not as time sensitive for higher sample rates (note-on graph, time interval is 2hours) (see MC_L pdf). Perhaps the levinson 64Hz sample rate filter doesn't do as well as time passes for these signals. When the filter didn't do well, the max(rms(residual)) seemed to increase with N.
-For 512Hz sample rate filter the max(rms(residual)) decreased with time. If the max(rms(residual)) were an indication of filter performance, it would mean that the 512Hz filter calculated at the initial time was performing better later as hours passed by! Perhaps max(rms(residual)) isn't always great at indicating filter performance.

Programming notes
-I had to modify values in do_all_time_lev.m to get the program to loop over the srates,N's,times I wanted
-do_all_time_lev.m is not as clean as do_all_lev.m
-for making the plots do_all_lev.m (which isn't really a procedure and is messy) has some examples of how to plot things from do_all_time_lev.m.
Attachment 1: MC_F.pdf
MC_F.pdf MC_F.pdf MC_F.pdf
Attachment 2: MC_L.pdf
MC_L.pdf MC_L.pdf MC_L.pdf MC_L.pdf MC_L.pdf MC_L.pdf MC_L.pdf MC_L.pdf
Attachment 3: miso_filter_lev.m
function [s] = miso_filter_lev(N,srate,rat,z)
%MISO_FILTER_LEV(N,srate,z) uses miso_firlev to get levinson
%   FIR Wiener filter of order N-1, using impulse response of 
%   N/srate. z is a structure gotten from the get_data function. 
%   z(end) is the signal which is filtered using z(i) for all i.
%   'rat' is the fraction of z which will be put into filter
%   funtion. The data from z is downsampled using srate and 
%   detrended. Let rat=1. I don't have that part working yet.


... 107 more lines ...
Attachment 4: get_mic_data.m
function[z,t0,duration]=get_mic_data(t,d_t,d)
%get_mic_data gets data for'C1:IOO-MC_F', 'C1:PEM-AS_MIC,
% Example:  z = get_mic_data('now',120,60)
%  start time is 't- d_t' so  d_t should be given in seconds. t should be given
%  as a number like 893714452. d is duration in seconds. get_mic_data saves
%  data to a file in current directory named 'temp_mic'. You will be asked to
%  save file as 'mic_(start_time)_(duration)'.

duration = d;

... 32 more lines ...
Attachment 5: do_all_time_lev.m
function[r] = do_all_time_lev(n,t0,int,duration,N,srate,rat,order,time,MC_L,MC_F,sample_rate)
%do_all_time explores how filter performance changes with time, sample rate,
%and order of filter. Outputs data,noise estimate, structure of max
%rms error and other info. It uses get_data, miso_filter_lev, and miso_filter_int and retrives
%MC_Ldata or MC_Fdata for multiple times, calculates a miso_filter for initial-time data
%file, applies filter to the other data files, and keeps track of the...
%max(rms(residual)) for each filter. n+1 is number of data files. int is time interval between
%data files, t0 is start time, duration is duration of each data file, srate
%is the sample rate for which filter is calculated, n_N is number of orders
%of the filter you want the program to calculate,int_N is interval by which N
... 215 more lines ...
Attachment 6: do_all_lev.m
function[r] = do_all_lev(n,t0,int,duration,n_N,int_N,n_srate,int_srate,rat,MC_L,MC_F)
%do_all_lev explores how filter performance changes with time, sample rate,
%and order of filter. Outputs data,noise estimate, structure of max
%rms error and other info. It uses get_data, miso_filter_lev, and miso_filter_int and retrives
%MC_Ldata or MC_Fdata for multiple times, calculates a miso_filter for initial-time data
%file, applies filter to the other data files, and graphs the rms of the cost
%function vs time. n+1 is number of data files. int is time interval between
%data files, t0 is start time, duration is duration of each data file, srate
%is the sample rate for which filter is calculated, n_N is number of orders
%of the filter you want the program to calculate,int_N is interval by which N
... 283 more lines ...
Attachment 7: do_all_plot.m
function[r] = do_all_plot(r,x,v)
 %do_all_plot plots variables contained in r(structure from
 %do_all_time_lev).Plots error(r.B.y) vs x. x can be
 %'s'(srate),'N'(order),'t'(time),'p'(impulse response). v can be 's','N','t'. 
 %example: do_all_plot(r,'s','t') makes a plot of error vs srate for
 %different times.

kk=1

err_N_srate=0
... 388 more lines ...
Attachment 8: miso_filter_int.m
function [s] = miso_filter_int(s,y)
%miso_filter_int inputs a filter and a structure array of data sets y, applies filter to data, and
%outputs a structure with fields: ppos(signal frequ spectrum),perr(cost
%function frequ spectrum),pest(signal estimate frequency
%spectrum),f(frequency),target(signal),est_darm(noise estimate),t(time).
%data file for which filter has been calculated is s (obtained using miso_filter). 
%y consists of data structures which will be filtered using
%filter from s. Then the power spectrum of the difference between signal and filtered-data is
%graphed for all the data files of y for comparison too see how well filter performs
%over time. Note if you want to create a y, take z1,z2,z3,etc. structures
... 120 more lines ...
  1130   Wed Nov 12 11:14:59 2008 CarynDAQPSLMC temp sensor hooked up incorrectly
MC Temperature sensor was not hooked up correctly. It turns out that for the 4 pin LEMO connections on the DAQ like J13, J14, etc. the channels correspond to horizontal pairs on the 4 pin LEMO. The connector we used for the temp sensor had vertical pairs connected to each BNC which resulted in both the differential pairs on J13 being read by the channel.
To check that a horizontal pair 4 pin LEMO2BNC connector actually worked correctly we unlocked the mode cleaner, and borrowed a connector that was hooked up to the MC servo (J8a). We applied a sine wave to each of the BNCs on the connector, checked the J13 signal and only one of the differential pairs on J13 was being read by the channel. So, horizontal pairs worked.
  1142   Mon Nov 17 20:47:19 2008 CarynSummaryGeneralDrove MC at 28kHz to excite drum modes
Rana, Alberto and I observed drum mode frequencies at 23.221kHz(MC1), 28.039kHz(MC2), 28.222kHz(MC3) while driving the mode cleaner. We observed no peaks when we didn't drive the mode cleaner. We used the SR785 to send a ~80mV noise signal in the 28-28.2kHz band to the mode cleaner mirrors via 1Y4-MC1,2,3-POSIN. Then we looked at 1Y2-Mode Cleaner-Qmon on the SR785 and saw peaks.
  1143   Tue Nov 18 13:28:08 2008 CarynDAQIOOnew channel for MC drum modes
Alberto has added a channel for the Mode Cleaner drum modes.
C1:IOO-MC_DRUM1
sample rate-2048
chnum-13648
  1158   Sat Nov 22 10:55:51 2008 CarynConfigurationIOODrum modes Lock-In settings changed
I unhooked the MC Demod Board's Qmon signal from the Lock-In. Set the demodulation frequency to 31.11Hz with 1V amplitude, and
put the output into MC_DRUM1. DTT showed a ~30Hz peak. Dataviewer showed signal with amplitude ~20,000.
Otherwise the settings were as Rana had them: Time Constant-100us,24dB/Sensitivity-200us/Low Noise
Want to check if Lock-In frequency drifts.
  1189   Tue Dec 9 10:48:17 2008 CarynSummaryGeneralcalibrating the jenne laser: impedance mismatch?

We sent RFout of network analyzer to a splitter, with one side going back to the network analyzer and the other to the laser modulation input. We observed a rippled transfer function through the splitter. The ripple is probably due to reflection due to an impedance mismatch in the laser.
Attachment 1: reflection.png
reflection.png
  1528   Tue Apr 28 12:55:57 2009 CarynDAQPEMUnplugged Guralp channels

For the purpose of testing out the temperature sensors, I stole the PEM-SEIS_MC1X,Y,Z channels.

I unplugged Guralp NS1b, Guralp Vert1b, Guralp EW1b cables from the PEM ADCU(#10,#11,#12) near 1Y7 and put temp sensors in their place (temporarily).

  4422   Tue Mar 22 00:03:29 2011 BryanConfigurationGreen LockingPSL vs Y arm laser temperature pairing

 OK. Today we did the same type of measurement for the Y arm laser as was done for the X arm laser here: http://nodus.ligo.caltech.edu:8080/40m/3759 

And attached here is a preliminary plot of the outcome - oddities with adding on the fitted equations, but they go as follows

(Red)    T_yarm = 1.4435*T_PSL - 14.6222

(Blue)    T_yarm = 1.4223*T_PSL - 10.9818

(Green) T_yarm = 1.3719*T_PSL - 6.3917


 

 PSL_vs_Y_arm_Temperatures.png

It's a bit of a messy plot - should tidy it up later...

  4425   Tue Mar 22 19:03:45 2011 BryanConfigurationGreen LockingPSL vs Y arm laser temperature pairing

Quote:

 I'm going to take the easy question - What are the pink data points??

And I'm going to answer the easy question - they're additional beat frequency temperature pair positions which seem to correspond to additional lines of beat frequencies other than the three highlighted, but that we didn't feel we had enough data points to make it worthwhile fitting a curve.

It's still not entirely clear where the multiple lines come from though - we think they're due to the lasers starting to run multi-mode, but still need a bit of thought on that one to be sure...

  4437   Thu Mar 24 13:50:30 2011 BryanConfigurationGreen LockingY arm laser

 Just a quick update... the Lightwave laser has now been moved up to the end of the Y arm. It's also been mounted on the new mounting block and heatsinks attached with indium as the heat transfer medium.

A couple of nice piccies...IMG_0188.JPG

Attachment 2: IMG_0190.JPG
IMG_0190.JPG
  4439   Thu Mar 24 15:30:59 2011 BryanConfigurationGreen LockingPSL vs Y arm laser temperature pairing
Fine-grained temperature vs temperature data around the current operating point of the PSL laser.
 
The last set of data was taken in 1 degreeC steps, but we want a bit more detail to find out what happens around the current PSL operating point. So we took some data with a 0.1 degC resolution.

The good news is that we seem to be running in a linear region of the PSL laser with a degree or so of range before the PSL Innolight laser starts to run multi-mode. On the attached graph we are currently running the PSL at 32.26degrees (measured) which puts us in the lower left corner of the plot. The blue data is the Lightwave set temperature (taken from the display on the laser controller) and the red data is the Lightwave laser crystal measured temperature (taken from the 10V/degC calibrated diagnostic output on the back of the laser controller - between pins 2 and 4).

The other good news is that we can see the transition between the PSL laser running in one mode and running in the next mode along. The transition region has no data points because the PMC has trouble locking on the multi-mode laser output - you can tell when this is happening because, as we approach the transition the PMC transmitted power starts to drop off and comes back up again once we're into the next mode region (top left portion of the plot).

 

The fitted lines for the region we're operating in are:

Y_arm_Temp_meas = 0.95152*T_PSL + 3.8672

Y_arm_Temp_set = 0.87326*T_PSL + 6.9825

Temp_Beating_Day02_html_m2d719182.jpg

 

  4440   Thu Mar 24 16:33:32 2011 BryanConfigurationGreen LockingPSL vs Y arm laser temperature pairing

X_arm and Y_arm vs PSL comparison.

 

 

Just a quick check of the performance of the X arm and Y arm lasers in comparison to the PSL. Plotting the data from the X arm vs PSL and Y arm vs PSL on the same plot shows that the X arm vs the PSL has no observable trending of mode-hopping in the laser, while the Y arm vs the PSL does. Suspect this is due to the fact that the X arm and PSL are both Innolight lasers with essentially identical geometry and crystals and they'll tend to mode-hop at roughly the same temperatures - note that the Xarm data is rough grained resolution so it's likely that any mode-hop transitions have been skipped over. The Lightwave on the other hand is a very different beast and has a different response, so won't hop modes at the same temperatures.

Given how close the PSL is to one of the mode-transition regions where it's currently operating (32.26 degC) it might be worth considering shifting the operating temperature down one degree or so to around 31 degC? Just to give a bit more headroom. Certainly worth bearing in mind if problems are noticed in the future.

PSL_vs_X-end_T_data_fine.jpg

  4464   Wed Mar 30 19:43:33 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

Right. I've got a whole load of info and data and assorted musings I've been saving up and cogitating upon before dumping it into these hallowed e-pages. there's so much I'll probably turn it into a threaded entry rather than put everything in one massive page.

An overview of what's coming:

I started out using http://lhocds.ligo-wa.caltech.edu:8000/40m/Advanced_Techniques/Green_Locking?action=AttachFile&do=get&target=modematch_END.png as a reference for roughly what we want to achieve... and from http://nodus.ligo.caltech.edu:8080/40m/100730_093643/efficiency_waist_edit.png we need a waist of about 50um at the green oven. Everything else up to this point is pretty much negotiable and the only defining things that matter are getting the right waist at the doubling oven with enough available power and (after that point) having enough space on the bench to separate off the green beam and match it into the Y arm.

 

So…

Step 1: Measure the properties of the beam out of the laser. Really just need this for reference later because we'll be using more easily measurable points on the bench.


Step 2:
Insert a lens a few cm from the laser to produce a waist of about of a few 100um around the Faraday. Note that there's really quite a lot of freedom here as to where the FI has to be - on the X arm it's around columns 29/30 on the bench, but as long as we get something that works we can get it closer to the laser if we need to.


Step 3:
After inserting the FI need to measure the beam after it (there *will* be some distortion and the beam is non-circular to begin with)


Step 3b:
If beam is non-circular, make it circular.


Step 4:
Insert a lens to produce a 50um waist at the doubling oven position. This is around holes 7/8 on the X arm but again, we're free to change the position of the oven if we find a better solution. The optical set-up is a little bit tight near that side of the bench on the X end so we might want to try aiming for something a bit closer to the middle of the bench? Depends how the lenses work out, but if it fits on the X end it will fit on the Y end.

 
Oh... almost forgot. While I've been doing most of the grunt-work and heavy lifting - thanks go out to Suresh, Kiwamu, Koji, Steve and everyone else who's helped out with discussion of results and assorted assists to numerous to mention.

 

  4465   Wed Mar 30 19:54:19 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

RIght! Overview out of the way - now comes the trivial first bit

 

Step 1: Beam out of the laser - this will be tricky, but we'll see what we can actually measure in this set-up. Can't get the Beamscan head any closer to the laser and using a lambda/2 plate + polariser to control power until the Faraday isolator is in place. Using 1 inch separation holes as reference points for now - need better resolution later, but this is fine for now and gives an idea of where things need to go on the bench. The beam is aligned to the 3rd row up (T) for all measurements, the Beamscan spits out diameters (measuring only the 13.5% values) so convert as required to beam radius and the beam is checked to ensure a reasonable Gaussian profile throughout.

 

Position A1_13.5%_width A2_13.5%_width

(bench) (um mean) (um mean)

32 2166.1 1612.5

31 2283.4 1708.3

30 2416.1 1803.2

29 2547.5 1891.4

27 2860.1 2070.3

26 2930.2 2154.4

25 3074.4 2254.0

24 3207.0 2339.4

 

OK. As expected, this measurement is in the linear region of the beampath - i.e. not close to the  waist position and beyond the Rayleigh length) so it pretty much looks like two straight lines. There's no easy way to get into the path closer to the laser, so reckon we'll just need to infer back from the waist after we get a lens in there. Attached the plot, but about all you really need to get from this is that the beam out of the laser is very astigmatic and that the vertical axis expands faster than the horizontal.

Not terribly exciting, but have to start somewhere.

 

laser_output_non_circular.png

 

 

 

  4466   Wed Mar 30 20:08:34 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

Step 2: Getting the beam through the Faraday isolator (FI).

Started out with an f=100mm lens at position 32,T on the bench which gave a decent looking waist of order 100 um in the right sort of position for the FI, but after checking the FI specs, it's limited to 500W/cm^2. In other words, if we have full power from the laser passing into it we'd need a beam width of more than 211 um. Solution? Use an f=150mm lens instead and don't put the FI at the waist. I normally don't put a FI at a waist anyway, for assorted reasons - scattering, thermal lensing, non-linear magnetic fields, the sharp changing of the field components in an area where you want as constant a beam as possible.  Checked with others to make sure they don't do things differently around these parts… Koji says it doesn't matter as long as it passes cleanly through the aperture. So… next step is inserting the Faraday.

The beam profiles in vertical and horizontal around the FI position with the f=150mm lens in place are attached. Note that the FI will be going in at around 0.56m.

Beam_Matching_02c_Vertical.pngBeam_Matching_02c_Horizontal.png

 

 

 

  4467   Wed Mar 30 20:14:17 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

Additional:

I fired up some old waistplotter routines, and set the input conditions as the measured waist after the lens and used that to work out what the input waist is at the laser. It may not be entirely accurate, but it /will/ be self consistent later on.

 

Vertical waist      = 105.00 um at 6.282 cm after laser output (approx)

Horizontal waist = 144.63 um at 5.842 cm after laser output (approx)

 

Definitely astigmatic.

 

  4468   Wed Mar 30 20:31:30 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

Step 3: Inserting FI and un-eliptical-ification of the beam

The FI set up on it's mount and the beam passes through it - centrally through the apertures on each side. Need to make sure it doesn't clip and also make sure we get 93% through (datasheet specs say this is what we should achieve). We will not achieve this, but anything close should be acceptable.

Setting up for minimum power through the FI is HWP @125deg.

Max is therefore @ 80deg

 

Power before FI = 544 mW

Power after FI =     496 mW (after optimising input polarisation)

Power dumped at input crystal = 8.6mW

Power dumped at input crystal from internal reflections etc = 3.5mW

Power dumped at output crystal on 1st pass = approx 8mW

 

OK. that gives us a 90.625% transmission and a 20.1mW absorption/unexplained loss.

 

Well - OK. The important part about isolators isn't their transmission, it's about how well they isolate. Let's see how much power gets ejected on returning through the isolator…

 

Using a beam splitter to pick off light going into and returning from the FI. A 50/50 BS1-1064-50-1025-45P. And using a mirror near the waist after the FI to send the beam back through. There are better ways to test the isolation performance of FI's but this will suffice for now - really only want to know if there's any reasonable isolation at all or if all of the beam is passing backwards through the device.

 

Power before BS = 536 mW (hmmn - it's gone down a bit)

Power through BS = (can't access ejected on first pass)

Power through FI = 164 mW (BS at odd angle to minimise refractive effect so less power gets through)

Power lost through mirror = 8.3mW (mirror is at normal incidence so a bit transmissive)

 

Using earlier 90.6% measurement as reference, power into FI = 170.83 mW

So BS transmission = 170.83/536 = 0.3187

BS reflectivity therefore = 1 - 0.3187 = 0.6813

 

Power back into FI = Thru FI - Thru mirror = 155.7 mW

 

Power reflected at BS after returning through FI = 2.2mW

Baseline power at BS reflection from assorted internal reflections in FI (blocked return beam) = 1.9mW

Note - these reflections don't appear to be back along the input beam, but they *are* detectable on the power meter.

 

Actual power returning into FI that gets reflected by BS = 0.3 mW

(note that this is in the fluctuating noise level of measurement so treat as an upper limit)

 

Accounting for BS reflectivity at this angle, this gives a return power = 0.3/0.6813 = 0.4403 mW

 

Reduction ratio (extinction ratio) of FI =  0.4403/155.7 = 0.00282

 

Again - note that this upper limit measurement is as rough and ready as it gets. It's easy to optimise this sort of thing later, preferable on a nice open bench with plenty of space and a well-calibrated photodiode. It's just to give an idea that the isolator is actually isolating at all and not spewing light back into the NPRO.

 

Next up… checking the mode-matching again now that the FI is in place. The beam profile was scanned after the FI and the vertical and horizontal waists are different...

  4469   Wed Mar 30 20:50:43 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

Step 3b: Non-circular? We can fix that...

A quick Beamscan sweep of the beam after the Faraday:

Position A1_13.5%_width A2_13.5%_width

(bench) (um mean) (um mean)

25.8 503.9 478.8

25 477.5 489.0

24 447.1 512.4

21 441.6 604.5

20 476.3 645.4

19 545.4 704.1

18 620.3 762.8

 

After_Faraday.png

 

OK. It looks not too bad - doesn't look too different from what we had. Note that the x axis is in local table units - I found this useful for working out where things were relative to other things (like lenses and the FI) - but it means the beam propagates from right to left in the plot. in other words, the horizontal waist occurs first and is larger than the vertical waist. Also - they're not fitted curves - they're by-eye, best guesses and there's no solution for the vertical that doesn't involve offsets... discussion in a later part of the thread.

 

Anyway! The wonderful thing about this plot is that the horizontal and vertical widths cross and the horizontal focussing at this crossing point is shallower than the vertical. This means that we can put a lens in at the crossing point and rotate it such that the lens is stronger in the horizontal plane. The lens can be rotated until the effective horizontal focal length is right to fix the astigmatism.

 

 

I used a 200mm lens I had handy - a rough check sweeping the Beamscan quickly indicated should be about right though. Adjusting the angle until the beam size at a distant point is approx circular - I then move the profiler and adjust again. Repeat as required. Now… taking some data. with just that lens in:

 

Position A1_13.5%_width A2_13.5%_width

(bench) (um mean) (um mean)

24 371.7 366.1

21 360.3 342.7

20 447.8 427.8

19 552.4 519.0

18 656.4 599.2

17 780.1 709.9

16 885.9 831.1

 

After_Faraday_and_Rotated_Lens.png

 

Well now. That looks quite OK. Fit's a bit rubbish on vertical but looks like a slight offset on the measurement again.

The angle of the lens looks awful, but if it's stupid and it works then it isn't stupid. If necessary, the lens can be tweaked a bit more, but there's always more tweaking possible further down the line and most of the astigmatic behaviour has been removed. It's now just a case of finding a lens that works to give us a 50 um beam at the oven position...

 

 

  4470   Wed Mar 30 21:21:15 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

Step 4: Matching into the oven

 

 

Now that the astigmatism is substantially reduced, we can work out a lens solution to obtain a 50um waist *anywhere* on the bench as long as there's enough room to work with the beam afterwards. The waist after the Faraday and lens is at position 22.5 on the bench. A 50 mm lens placed 18 cm after this position (position 14.92 on the bench) should give a waist of 50 um at  24.57 cm after the waist (position 12.83 on the bench). This doesn't give much room to measure the beam waist in though - the Beamscan head has a fairly large finite size… wonder if there's a slightly less strong lens I could use…

OK. With a 66 mm lens at 23 cm (position 13.45 on the bench) after the waist we get a 50 um waist at 31.37 cm after the waist (position 10.15 on the bench). 

 

Oven_Lens_Solution_66mm.png

 

Closest lens I found was 62.9mm which will put the 50um point a bit further towards the wall, but on the X-arm the oven is at position 8.75 ish. So anything around there is fine.

 

Using this lens and after a bit of manual fiddling and checking with the Beamscan, I figured we needed a close in, fine-grained measurement so set the Beamscan head up on a micrometer stage Took a whoie bunch of data around position 9 on the bench:

 

 

Position A1_13.5%_width A2_13.5%_width

(mm) (um mean) (um mean)

-15 226.8 221.9

-14 210.9 208.3

-13 195.5 196.7

-12 181.0 183.2

-11 166.0 168.4

-10 154.0 153.1

-9 139.5 141.0

-8 127.5 130.0

-7 118.0 121.7

-6 110.2 111.6

-5 105.0 104.8

-4 103.1 103.0

-3 105.2 104.7

-2 110.9 110.8

-1 116.8 117.0

0 125.6 125.6

0 125.6 125.1

1 134.8 135.3

2 145.1 145.6

3 155.7 157.2

4 168.0 168.1

5 180.5 180.6

6 197.7 198.6

7 211.4 209.7

8 224.0 222.7

9 238.5 233.7

10 250.9 245.8

11 261.5 256.4

12 274.0 270.4

13 291.3 283.6

14 304.2 296.5

15 317.9 309.5

 

Matching_Into_Green_Oven_zoomed_out.pngMatching_Into_Green_Oven_zoomed_in.png

 

And at this point the maximum power available at the oven-waist is 298mW. With 663mW available from the laser with a desired power setting of 700mW on the supply. Should make sure we understand where the power is being lost. The beam coming through the FI looks clean and unclipped, but there is some stray light around.

 

Position A1_13.5%_width A2_13.5%_width

(bench) (um mean) (um mean)

7 868.5   739.9

6 1324 1130

5 1765 1492

4 2214 1862

 

The plot looks pretty good, but again, there looks to be an offset on the 'fitted' curve. Taking a couple of additional points further on to make sure it all works out as the beam propagates. I took a few extra points at the suggestion of Kiwamu and Koji - see the zoomed out plot.  The zoomed in plot has by-eye fit lines - again, because to get the right shape to fit the points there appears to be an offset. Where is that coming from? My suspicion is that the Beamscan doesn't take account of the any background zero offsets when calculating the 13.5% and we've been using low power when doing these measurements - very small focussed beams and didn't want to risk damage to the profiler head.

 

Decided to take a few measurements to test this theory. Trying different power settings and seeing if it gives different offset and/or a changed width size

 

7 984.9 824.0 very low power

7 931.9 730.3 low power

7 821.6 730.6 higher power

7 816.4 729.5 as high as I'm comfortable going

 

Trying this near the waist…

 

8.75 130.09 132.04 low power

8.75 106.58 105.46 higher power

8.75 102.44 103.20 as high as it can go without making it's saturated

 

So it looks like offset *is* significant and the Beamscan measurements are more accurate with more power to make the offsets less significant. Additionally, if this is the case then we can do a fit to the previous data (which was all taken with the same power setting) and simply allow the offset to be a free parameter without affecting the accuracy of the waist calculation. This fit and data coming to an e-log near you soon.

 

Of course, it looks from the plots above (well... the code that produces the plots above) that the waist is actually a little bit small (around 46um) so some adjustment of the last lens back along the beam by about half a cm or so might be required.

 
  4476   Thu Mar 31 14:10:00 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

Quote:

 I went through the entries.

1. Give us a photo of the day. i.e. Faraday, tilted lens, etc...

2. After all, where did you put the faraday in the plot of the entry 4466?

3. Zoomed-in plot for the SHG crystal show no astigmatism. However, the zoomed out plot shows some astigmatism.
How consistent are they? ==> Interested in seeing the fit including the zoomed out measurements.

 OK. Taking these completely out of order in the easiest first...

2. The FI is between positions 27.75 and 32 on the bench - i.e. this is where the input and output apertures are. (corresponds to between 0.58 and 0.46 on the scale of those two plotsand just before both the vertical and horizontal waists) At these points the beam radius is around 400um and below, and the aperture of the Faraday is 4.8mm (diameter).

1. Photos...

Laser set up - note the odd angles of the mirrors. This is where we're losing a goodly chunk of the light. If need be we could set it up with an extra mirror and send the light round a square to provide alignment control AND reduce optical power loss...

P3310028.JPG

 

Faraday and angled lens - note that the lens angle is close to 45 degrees. In principle this could be replaced with an appropriate cylindrical lens, but as long as there's enough light passing through to the oven I think we're OK.

P3310029.JPG

3. Fitting... coming soon once I work out what it's actually telling me. Though I hasten to point out that the latter points were taken with a different laser power setting and might well be larger than the actual beam width which would lead to astigmatic behaviour.

  4477   Thu Mar 31 15:23:14 2011 BryanConfigurationGreen LockingThe wonderful world of mode-matching

Quote:

3. Zoomed-in plot for the SHG crystal show no astigmatism. However, the zoomed out plot shows some astigmatism.

How consistent are they? ==> Interested in seeing the fit including the zoomed out measurements.

Right. Fitting to the data. Zoomed out plots first. I used the general equation f(x) = w_o.*sqrt(1 + (((x-z_o)*1064e-9)./(pi*w_o.^2)).^2)+c for each fit which is basically just the Gaussian beam width parameter calculation but with an extra offset parameter 'c'

Vertical fit for zoomed out data:

Coefficients (with 95% confidence bounds):

       c =   7.542e-06  (5.161e-06, 9.923e-06)

       w_o =   3.831e-05  (3.797e-05, 3.866e-05)

       z_o =       1.045  (1.045, 1.046)

 

Goodness of fit:

  SSE: 1.236e-09

  R-square: 0.9994

 
Horizontal fit for zoomed out data:
 

Coefficients (with 95% confidence bounds):

       c =   1.083e-05  (9.701e-06, 1.195e-05)

       w_o =   4.523e-05  (4.5e-05, 4.546e-05)

       z_o =       1.046  (1.046, 1.046)

 

Goodness of fit:

  SSE: 2.884e-10

  R-square: 0.9998

  Adjusted R-square: 0.9998

  RMSE: 2.956e-06

 

Zoomed_out_fitting01.png

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

 

OK. Looking at the plots and residuals for this, the deviation of the fit around the waist position, and in fact all over, looks to be of the order 10um. A bit large but is it real? Both w_o values are a bit lower than the 50um we'd like, but… let's check using only the zoomed in data -  hopefully more consistent since it was all taken with the same power setting.

 

 

Vertical data fit using only the zoomed in data:

 

Coefficients (with 95% confidence bounds):

       c =   1.023e-05  (9.487e-06, 1.098e-05)

       w_o =   4.313e-05  (4.252e-05, 4.374e-05)

       z_o =       1.046  (1.046, 1.046)

 

Goodness of fit:

  SSE: 9.583e-11

  R-square: 0.997

 

Horizontal data fit using only the zoomed in data:

 

Coefficients (with 95% confidence bounds):

       c =   1.031e-05  (9.418e-06, 1.121e-05)

       w_o =    4.41e-05  (4.332e-05, 4.489e-05)

       z_o =       1.046  (1.046, 1.046)

 

Goodness of fit:

  SSE: 1.434e-10

  R-square: 0.9951

 

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Zoomed_in_fitting01.png

 

The waists are both fairly similar this time 43.13um and 44.1um and the offsets are similar too  - residuals are only spread by about 4um this time.

 

I'm inclined to trust the zoomed in measurement more due to the fact that all the data was obtained under the same conditions, but either way, the fitted waist is a bit smaller than the 50um we'd like to see. Think it's worthwhile moving the 62.9mm lens back along the bench by about 3/4 -> 1cm to increase the waist size.

 

 

 

 

 

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