After the vent, the IPang spot position on the steering mirrors on the Yend table moved approximately by 1 inch down.

Inside the chamber, the spot position is in the center of the steering mirror. (difficult to take a picture because the PSL beam power has been reduced)

 Yend table picture updated on the wiki page

I did a calibration measurement for the Y part of the BeatBox using a Marconi. This is in order to get a more accurate calibration for the arm cavity scan measurement.

The calibration factor I found is:

C1:ALS-BEATX_FINE_PHASE_OUT   50.801 +/- 0.009 deg/MHz

Procedure

During my cavity scan measurement, I had recorded the beat frequency and amplitude from the Spectrum Analyzer at each zero crossing.

I connected the Marconi to the RF in of the Y part of the BeatBox, and I set the Marconi carrier frequency at one of this zero-crossing frequency that I had recorded, while I set the amplitude in way to have on the spectrum analyzer the same beat amplitude that I read during the measurements or, equivalently, in order to have C1:ALS_BEATY_FINE_Q of the order of 1200 (which is the same value I had during my measurements).

I started with

• Carrier frequency = 80.2 MHz
• Amplitude = -3dBm

Then I monitored the C1:ALS_BEATY_FINE_I on the oscilloscope and I adjusted the carrier frequency so that I had zero signal on the oscilloscope. Eventually the frequency corresponding to the zero crossing was 79.989 MHz.

I resetted the phase (clear history in the BEATY_FINE_PHASE panel) and I started changing the frequency by steps of 0.2 MHz, and I spanned about 70 MHz (from 32 to 102 MHz).

Resutls

The calibration coefficient I found is not so different from the one that Yuta measured (elog 8199).

Here are the fit parameters:

y = a + bx

a = -4239.7 +/- 0.6 deg

b = 50.801 +/- 0.009 deg/MHz

I tried to put together a rudimentary heater setup. 

As a heating element, I used the soldering iron tip heated up to ~800°C.

To make a reflector, I used the small basket which holds the cork of champains battles (see figure 1), and I covered it with alumnum foil. Of course, it cannot be really considered as a parabolic reflector, but it's something close (see figure 2).

Then, I put a ZnSe 1 inch lens, 3.5 inch FL (borrowed from TCS lab) right after the reflector, in order to collect as much as possible the radiation and focus it onto an image (figure 3). In principle, if the heat is collimated by the reflector, the lens should focus it in a pretty small image. Finally, in order to see the image, I put a screen and a small piece of packaging sponge (because it shouldn't diffuse too much), and I tried to see the projected pattern with a thermal camera (also borrowed from Aidan). However, putting the screen in the lens focal plane didn't really give a sharp image, maybe because the reflector is not exactly parabolic and the heater not in its focus. However, light is still focused on the focal plane, although the image appears still blurred. Perahps I should find a better material (with less dispersion) to project the thermal image onto. (figure 4)

Finally, I measured the transmitted power with a broadband power meter, which resulted to be around 10mW in the focal plane. 

I made some simulation to study the change that the heater setup can induce on the Radius of Curvature of the ETM.

Heat pattern

First, I used a non-sequential ray tracing software (Zemax) to calculate the heat pattern. I made a CAD of the elliptical reflector and I put a radiative element inside it (similar to the rod-heater 30mm long, 3.8mm diameter that we ordered), placing it in such a way that the heater tip is as close as possible to the ellipse first focus. (figure 1)

Then, by putting a screen at the second focus of the ellipse (where we suppose to place the mirror HR surface), I could find the projected heat pattern, as shown in figure 2 and 3 (section). Notice that the scale is in INCH, even if the label says mm. As you can see, the heat pattern is pretty broad, but still enough to induce a RoC change. 

Mirror deformation

In order to compute the mirror deformation induced by this kind of pattern, I used this map produced with Zemax as absorption map in COMSOL. I considered ~1W total power absorbed by the mirror (just to have a unitary number).

The mirror temperature and deformation maps induced by this heat pattern are shown in figures 4 and 5. 

RoC change evaluation

Then I had to evaluate the RoC change. In particular, I did it by fitting the Radius of Curvature over a circle of radius:

where  is the waist of tha Gaussian mode on the ETMY (5mm) and n is the mode order. This is a way to approximately know which is the Radius of Curvature as "seen" by each HOM, and is shown in figure 6 (the RoC of the cold mirror is set to be 57.37m). Of course, besides being very tiny, the difference in RoC strongly depends on the heat pattern.

Gouy phase variation

Considering this absorbed power, the cavity Gouy phase variation between hot and cold state is roughly 15kHz (I leave to the SURFs the details of the calculation).

Unanswered points

So the still unaswered questions are:

- which is the minimum variation we are able to resolve with our measurement

- how much heating power do we expect to be projected onto the mirror surface (I'll make another entry on that)

[Annalisa, Koji]

Today both the heater and the reflector were delivered, and we set down the setup to make some first test.

The schematic is the usual: the rod heater (30mm long, 3.8 mm diameter) is set inside the elliptical reflector, as close as possible to the first focus. In the second focus we put the power meter in order to measure the radiated power. The broadband power meter wavelength calibration has been set at 4µm: indeed, the heater emits all over the spectrum with the Black Body radiation distribution, and the broadband power meter measures all of them, but only starting from 4µm they will be actually absorbed my the mirror, that's why that calibration was chosen.

We measured the cold resistance of the heater, and it was about 3.5 Ohm. The heater was powered with the BK precision DC power supply 1735, and we took measurements at different input current.

We also aimed at measuring the heater temperature at each step, but the Fluke thermal camera is sensitive up to 300°C and also the FLIR seems to have a very limited temperature range (150°C?). We thought about using a thermocouple, but we tested its response and it seems definitely too slow. 

Some pictures of the setup are shown in figures 1 and 6.

Then we put an absorbing screen in the suspension mount to see the heat pattern, in such a way to get an idea of the heat spot position and size on the ETMY. (figure 2)

The projected pattern is shown in figures 3-4-5

The optimal position of the heater which minimizes the heat beam spot seems when the heater inserted by 2/3 in the reflector (1/3 out). However, this is just a qualitative evaluation.

Finally, two more pictures showing the DB connector on the flange and the in-vacuum cables.

Some more considerations about in-vacuum cabling to come.

Steve: how are you going to protect the magnets ?

[Annalisa, Rana]

In order to power the heater setup to be installed in the ETMY chamber, we took the Sorensen DSC33-33E power supply from the Xend rack which was supposed to power the heater for the seismometer setup.

We modified the J3 connector behind in such a way to allow a remote control (unsoldered pins 9 and 8). 

Now pins 9 and 12 need to be connected to a BNC cable running to the EPICS.

RXA update: the Sorensen's have the capability to be controlled by an external current source, voltage source, or resistive load. We have configured it so that 0-5V moves the output from 0-33 V. There is also the possibility to make it a current source and have the output current (rather than voltage) follow the control voltage. This might be useful since out heater resistance is changing with temperature.

[Gautam, Johannes, Koji, Annalisa]

Tonight we increased the power of the PSL laser and we achieved the lock of both arms with high power.

The AUX beam alignment to the Y arm was recovered and the PLL restored (using the Marconi as LO).

We made a quick measurement of the phase noise and the results will be posted tomorrow.

The beam on the PSL has been blocked, as well as the AUX beam on the AS table. The Marconi has been switched off.

gautam:

1. Before turning up PSL power, I placed a block in front of MC refl to avoid any PD burning. Replaced HR Y1 2" optic with the usual 10% reflective BS to direct MC REFL to the locking PD.
2. Waveplate was rotated back to 180 deg (original position before the vent). After optimizing PMC transmission, I measured 1.05 W going into the IMC (pre-vent value was 1.07 W, prolly within power meter absolute accuracy).
3. IMC autolocker restored to usual high power version on megatron.
4. There seems to be some kind of vacuum interlock in effect that prevents me from opening the PSL shutter via EPICS - I had to toggle the position on the shutter controller under the table. After tonight's work, I returned the controller to the NC state, to avoid any further interference with this interlock code that may prevent pumping in the AM.
5. PLL gain was re-adjusted to achieve maximum stability (judged by eye) of the beat-note in lock triggered on the Marconi LO signal. Alignment onto the NF beatPD was also tweaked to squeeze out as much beat as possible.
6. The main objective tonight was to send AUX beam in, recover transmission beat, scan the AUX frequency, and resolve some peaks (MAX HOLD scanning technique, magnitude only for now, no phase info). Thanks to JE's expert fiber alignment and beatnote maximization, we achieved this . Annalisa will post a plot tmr. 
7. For unknown reasons, the Y arm ASS does not maximize TRY. So we are in the unfortunate situation of neither arm having a working ASS servo. To be worked on later.

The schematic of the homodyne configuration is shown below.

Following are the list of components

• The fiber mismatch between the couplers and the delay fiber could affect the coupling efficiency

Attachment #1 shows the schematic of the test setup. Signal generator (Marconi) was used to supply the RF input. We observed the IF output in the following three test conditions.

1. Observed the spectrum with FM modulation (fcarrier of 40 MHz and fmod of 221 Hz )- a peak at 221 Hz was observed.
2. Observed the noise spectrum without FM modulation.
3. Observed the noise spectrum after disconnecting the delayed output of the delay line. 

• It is observed that the broad band noise level is higher without FM modulation (2) compared to that we observed after disconnecting the delayed output of the delay line (3).
• It is also observed that the noise level is increasing with increase in RF input power. 
• We need to find the reason for increase in broad band noise .

We characterized the power splitter ( Minicircuit- ZAPD-2-252-S+). The schematic of the measurement setup is shown in attachment #1. The network/spectrum/impedance analyzer (Agilent 4395A) was used in the network analyzer mode for the characterisation. The RF output is enabled in the network analyser mode. We used an other spliiter (Power splitter #1) to splitt the RF power such that one part goes to the network analzer and the other part goes to the power spliiter (Power splitter #2) . We are characterising power splitter #2 in this test. The characterisation results and comparison with the data sheet values are shown in Attachment # 2-4.

Attachment #2 : Comparison of total loss in port 1 and 2

Attachment #3 : Comparison of amplitude unbalance

Attachment #4 : Comparison of phase unbalance

• From the data sheet: the splitter is wideband, 5 to 2500 MHz, useable from 0.5 to 3000 MHz. We performd the measurement from 1 MHz to 500 MHz (limited by the band width of the network analyzer).
• It can be seen from attachment #2 and #4 that there is a sudden increase below ~11 MHz. The reason for this is not clear to me
• The mesured total loss value for port 1 and port 2 are slightly higher than that specified in the data sheet.From the data sheet, the maximum loss in port 1 and port 2 in the range at 450 MHz are 3.51 dB and 3.49 dB respectively. The measured values are 3.61 dB and 3.59 dB respectively for port 1 and port 2, which is higher than the values mentioed in the data sheet. It can also be seen from attachment #1 (b) that the expected trend in total loss with frequency is that the loss is decreasing with increase in frequency and we are observing the opposite trend in the frequency range 11-500 MHz. 
• From the data sheet, the maximum amplitude balance in the 5 MHz-500 MHz range is 0.02 dB and the measured maximum value is 0.03 dB
• Similary for the phase unbalance, the maximum value specified by the data sheet in the 5 MHz- 500 MHz range is 0.12 degree and the measurement shows a phase unbalance upto 0.7 degree in this frequency range
• So the observations shows that the measured values are slighty higher than that specified in the data sheet values.

The goal was to characterise the new amplifier (AP1053). For a practice, I did the characterisation of the old amplifier.This test is similar to that reported in Elog ID 13602.

• Attachment #1 shows the schematic of the setup for gain characterisation and Attachment #2 shows the results of gain characterisation. 
• The gain measurement is comparable with the previous results. From the data sheet, 10 dB gain is guaranteed in the frequency range 10-450 MHz. From our observation, the gain is not flat pver this region. We have measured a maximum gain of 10.7 dB at 6 MHz and it has then decreased upto 8.5 dB at 500 MHz
• Attachement #3 shows the schematic of the setup for the noise characterisation and Attachment # 4 shows the results of noise measurment. 
• The noise measurement doesn't look fine. We probably have to repeat this measurement.

• Attachment #1 shows the schematic of the experimental setup for the frequency noise measurement of 1 um laser source.

• AUX laser will be used as the seed source and it is already coupled to a 60 m fiber (PM980). The other end of the fiber was at the AS table and we have now removed it and placed in the PSL table.

• Attachment # 2 shows the photograph of the experimental setup. The orange line shows the beam that is coupled to the delayed arm of MZI and the red dotted line shows the undelayed path.

• As mentioned, AUX is already coupled to the 60 m fiber and the other end of the fiber is now moved to the PSL table. This end needs to be collimated. We are planning to take the same collimator from AS table where it was coupled into before. The position where the collimator to be installed is shown in attachment #2. Also, we need to rotate the mirror (as indicated in attachment #2) to get the delayed beam along with the undelayed beam and then to combine them. As indicated in attachment #2, we can install one more photo diode to perform  balanced detection.

• We need to decide on which photodetector to be used. It could be NF1801 or PDA255.

• We also performed the power measurement at different locations in the beam path. The different locations at which power measurement is done is shown attachment #3

• There is an AOM in the beam path that coupled to the delayed arm of MZI. The output beam after AOM was coupled to the zero-order port during this measurement. That is the input voltage to the AOM was at 0 V, which essentially says that the beam after the AOM is not deflected and it is coupled to the zero-order port. The power levels measured at different locations in this condition are as follows. A)282 mW B)276 mW C)274 mW D)274 mW E)273 mW F)278 mW G)278 mW H)261 mW I)263 mW J)260 mW K)131 mW L)128 mW M)127 mW N)130 mW

• It can be seen that the power is halved from J to K. This because of a neutral density filter in the path of the beam

• In this case, we measured a power of 55 mW at the output of the delayed fiber. We then adjusted the input voltage to the AOM driver to 1 V such that the output of AOM is coupled to the first order port. This reduced the power level in the zero-order port of AOM that is coupled to the delayed arm of the MZI. In this case we measured a power of 0.8 mW at the output of delayed fiber.

•  We must be careful about the power level that is reaching the photodetector such that it should not exceed the damage threshold of the detector.

• The power measured at the output of undelayed path is 0.8 mW.

• We also must place the QWP and HWP in the beam path to align the polarisation.

• Attachment #1 shows the present experimental setup. The photodiode is now replaced with PDA255. The farther end of the fiber (output of the delayed arm) is coupled through a collimator and aligned such that the beam from the delayed path fall on the detector along with the undelayed path of MZI. We tried to measure the frequency noise of the laser with this setup, but we didn’t get anything sensible.

• One of the main draw backs of the measurement was the polarisation was not aligned properly in the setup. So, then the next step was to identify the polarisation at different locations in the beam path and to maximise the polarisation to either S or P component.

• So, we introduced HWP at the input beam path after isolator as shown in attachment #1. Also, the polarisation was tested at positions P1, P2, P3, and P4 shown in attachment #1 by placing a polarisation beam splitter at these locations and then by observing the transmitted (P component) and reflected light (S component) using power meter.

• The observations at different locations are as the follows

• These observations show that the P and S components are almost equal, and this is not a good polarisation arrangement. At this point, we also had to check whether the incoming beam is linearly polarised or not.

• To test the same, the PBS was placed at position P1 and the P and S components were observed with power meter as the HWP is rotated.Attachment # 2 shows the results of the same, that is the variation in P and S component as the HWP is rotated.

• This result clearly shows that the input beam is linearly polarised. The HWP was then adjusted such that the P component is maximum and coupled to the MZI. With this orientation of HWP, the polarisation observed at different positions P1, P2, P3, and P4 are as follows.

• This shows that the polarisation is linearly polarised as well as it is oriented along the P direction (parallel to the optical table).

• We have the polarisation maintaining fiber (PM 980) as the delay fiber. The polarisation of the light as it propagates through a PM fiber depends on how well the input beam is coupled to the axis (slow or fast) of the fiber. So, the next task was to couple the light to one of the axes of the fiber.

• The alignment key on the fiber is a good indication of the axis of the fiber. In our case, the alignment key lines up with the slow axis of the fiber. We decided to couple the light to the fast axis of the fiber. Since the incoming beam is P polarised, the output fiber coupler was  aligned such that the fast axis is parallel to optical table as possible.

• A PBS was then introduced after the fiber output collimator . There is a HWP (marked as HWP2 in attachment 1) in front of the input coupler of the fiber as well. This HWP was then rotated and observed the P and S component from the PBS that is now placed after the output coupler with a power meter.The idea was , when the light is coupled to the fast axis of the fiber, we will see the maximum at the P componet at the output

• Attachment # 3 shows the observation. 

• In this way I tried to find the orientation of the HWP2 such that the P component is maximum at the output. But I was not succeeded in this method and observed that the output was fluctuating when the fiber was disturbed. One  doubt we had was whether the fiber is PM or not . Thus we checked the fiber end with fiber microscope and confirmed that it is PM fiber. 

• Thus, we modifed the setup as shown in attachement # 4.The photodetector (PDA55) was monitoring the S component and the output of the detector was observed on an oscilloscope. We rotated the HWP2 such that the S component is almost minimum. At the same time, we were disturbing the fiber and was observing whether the output is fluctuating. The HWP2 angle was tweaked around the minimum of S component and observed the output with disturbing the fiber. This way we found the orientation of HWP2  such that the light is coupled to the fast axis of the fiber and the output was not fluctuating while we disturb the fiber. We tested it  by heating the fiber with a heat gun as well and confirmed that the output is not fluctuating and thus the light is coupled to the fast axis of the fiber.

• The alignment of the output beam from the delayed path of MZI to the photodetector was disturbed when we did the polarisation characterisation yesterday. So, today we tried to align the output beam from the delayed path of MZI to the detector .
• We then observed the beat output from the detector on oscilloscope.We initialy observed a dc shift . We then applied a frequency modulation on the input laser and observed the output on oscilloscope. We expected to see variation in output frequency in accordance with variation of input frequency modulation. But we didnt observe this and we were not really getting the interference pattern. 
• We tried to make the alignment better. With a better alignment, we could see the interference pattern. We also observed that the output frequency was varying in accordance with variation in the input frequency modulation. We would expect a better result with proper mode matching of the two beams on the photodetector.

• Attachement #1 shows the input (ch4-green) modulation frequency and the photodiode output (ch1-yellow) when the modulation frequency is about 100 Hz
• Attachement #2 shows the input (ch4-green) modulation frequency and the photodiode output (ch1-yellow) when the modulation frequency is about 30 Hz
• The output frequency is varying in accordance with variation in modulation frequency. It is observed that, for a given modulation frequency also, the output frequency is fluctuating. There could be multiple reasons for this behaviour. One of the main reasons is the frequency noise of the laser itself. Also, there could be acoustic noise coupled to the system (eg, by change in length of the fiber).
• The experimental setup is then modified as shown in attachment #3. The thick beam spliiter is replaced with a thinner one. The mount is also changed such that the transmitted beam can be now coupled to an other photodiode (earlier  the transmitted light was blocked by the mount). One more photodiode (PDA55) is introduced .So now the two photodiodes in the setup are PDA520 and PDA 55. 
• We then applied frequency modulation on the input laser and observed the output of the two photodiodes. But we didn't get the results as we expected and observed earlier (shown in attachment #1 &2). Looks like, the problem is poor mode matching between the two beams. 

• Attchment #1,2,3 and 4 shows the results with frequency modulation of 32 Hz, 140 Hz , 300 Hz and without frequency modulation. I am trying to understand these results better.
• A lot of fringing is there even when no modulation is applied. We hope to improve this by spooling the fiber and then encasing it in a box. 
• As mentioned by Gautam, we have got a 50 m spooled fiber. Attachment #5 shows the photo of the same

The alignement was disturbed after the replcement of the beam splitter. We tried to get the alignment back . But we are not succeeded yet in getting good interfernce pattern. This is mainly because of poor mode matching of two beams. We will also try with the spooled fiber.

• Attachment #1 shows the time domain output from this measurement. The contrast between the maximum and minimum is better in this case compared to the previous trials.
• We also tried to extract the frequency noise of the laser from this measurement. Attachment #2 shows the frequency noise spectrum. The experimental result is compared with the theoretical value of frequency noise. Above 10 Hz, the trend is comparable to the expected 1/f characteristics, but there are other peak also appearing. Similarly, below 10 Hz, the experimentally observed value is higher compared to the theory.
• One of the uncertainties in this result is because of the length fluctuation of the fiber. The phase fluctuation in the system could be either because of the frequency noise of the laser or because of the length fluctuation of the fiber.  So,one of the reasons for the discrepancy between the experimental result and theory could be because of  fiber length fluctuation. Also, there were no locking method been applied to operate the MZI in the linear range.
• The next step would be to do a heterodyne measurement. Attachment #3 shows the schematic for the heterodyne measurement. A free space AOM can be inserted in one of the arms to do the frequency shift. At the output of photodiode, a RF heterodyne method as shown in attachment #3 can be applied to separate the inphase and quadrature component. These components need to be saved with a deep memory system. Then the phase and thus the frequency noise can be extracted.
• Attachment #4 shows the noise budget prepared for the heterodyne setup. The length of the fiber considered is 60 m and the photodiode is PDA255. I also have to add the frequency noise of the RF driver and the intensity noise of the laser in the noise budget.

My understanding is that the main advantage in going to the heterodyne scheme is that we can extract the frequecy noise information without worrying about locking to the linear region of MZI. Arctan of the ratio of the inphase and quadrature component will give us phase as a function of time, with a frequency offset. We need to to correct for this frequency offset. Then the frequency noise can be deduced. But still the frequency noise value extracted would have the contribution from both the frequency noise of the laser as well as from fiber length fluctuation. I have not understood the method of giving temperature feedback to the NPRO.I would like to discuss the same.

The functional form used for the curve labeled as theory is 5x10⁴/f. The power spectral density (V²/Hz) of the the data in attachment #1 is found using the pwelch function in Matlab and square root of the same gives y axis in V/rtHz. From the experimental data, we get the value of V_max and V_min. To ride from V_max to V_min , the corrsponding phase change is pi. From this information, V/rad can be calculated. This value is then multiplied with 2*pi*time dealy to get the quantity in V/Hz. Dividing V/rtHz value with V/Hz value gives  y axis in Hz/rtHz. The calculated value of shot noise and dark current noise are way below (of the order of 10^-4 Hz/rtHz) in this frequency range. 

I forgor to take the picture of the setup at that time. Now Andrew has taken the fiber beam splitter back for his experiment. Attachment #1 shows the current view of the setup. The data from the previous trial is saved in /users/anjali/MZ/MZdata_20190417.hdf5

It is noticed that one of the doors (door # 2 ) of the PSL table is broken. Attachement #1 shows the image

From the earlier results with homodyne measurement,the V_max and V_min values observed were comparable with the expected results . So in the time interval between these two points, the MZI is assumed to be in the linear region and I tried to find the frequency noise based  on data available in this region.This results is not significantly different from that we got before when we took the complete time series to calculate the frequency noise. Attachment #1 shows the time domain data considered and attachment #2 shows the frequecy noise extracted from that. 

As discussed, we will be trying the heterodyne method next. Initialy, we will be trying to save the data with two channel ADC with 16 kHz sampling rate. With this setup, we can get the information only upto 8 kHz. 

We repeated the homodyne measurement to check whether we are measuring the actual frequency noise of the laser. The idea was to repeat the experiment when the laser is not locked and when the laser is locked to IMC.The frequency noise of the laser is expected to be reduced at higher frequency  (the expected value is about 0.1 Hz/rtHz at 100 Hz ) when it is locked to IMC . In this measurement, the fiber beam splitter used is Non PM. Following are the observations

1. Time domain output_laser unlocked.pdf : Time domain output when the laser is not locked. The frequency noise is estimated from data corresponds to the linear regime. Following time intervals are considered to calculate the frequency noise (a) 104-116 s (b) 164-167 s (c) 285-289 s

2. Frequency_noise_laser_unlocked.pdf: Frequency noise when the laser is not locked. The model used has the functional form of 5x10⁴/f as we did before. Compared to our previous results, the closeness of the experimental results to the model is less from this measurement. In both the cases, we have the uncertainty because of the fiber length fluctuation. Moreover, this measurement could have effect of polarisation fluctuation as well.

3.Time domain output_laser locked.pdf :Time domain output when the laser is locked. Following time intervals are considered to calculate the frequency noise (a) 70-73 s (b) 142-145 s (c) 266-269 s. 

4. Frequency_noise_laser_locked.pdf : Frequency noise when the laser is locked

5. Frequency noise_comparison.pdf : Comparison of frequency noise in two cases. The two values are not significantly different above 10 Hz. We would expect reduction in frequency noise at higher frequency once the laser is locked to IMC. But this result may indicate that we are not really measuring the actual frequency noise of the laser.

I borrowed one Marconi (2023 B) from 40 m lab to QIL lab.

I am currently working on an optical arrangement consisting of a QPD that measures the fluctuations of an incoming HeNe laser beam that is reflected by a mirror. The goal is to add a second QPD to the optical arrangement to form a linear combination that effectively cancels out the (angular) fluctuations from the laser beam itself so that we can only focus on the fluctuations produced by the mirror.

In order to solve this problem, I have written a program for calculating the different contributions of the fluctuations of the HeNe laser and fluctuations from the mirror, for each QPD (program script attached). The goal of the program is to find the optimal combination of L0, L1, L2, and f2 that cancels the fluctuations from the laser beam (while retaining  solely the fluctuations from the mirror) when adding the fluctuations of QPD 1 and QPD 2 together. 

By running this program for different combinations of distances and focal lengths, I have found that the following values should work to cancel out the effects of the oscillations from the HeNe laser beam (assuming a focal length of 0.2 m for the lens in front of the original QPD):

• L0 = 1.0000 m (distance from laser tube to mirror)

• L1 = 0.8510 m (distance from mirror to lens in front of QPD 1)

• L2 = 0.9319 m (distance from beamsplitter to lens in front of QPD 2)

• f2 = 0.3011 m (focal length of lens in front of QPD 2)

Based on these calculations, I propose to try the following lens for QPD 2:

1’’ UV Fused Silica Plano-Convex Lens, AR-Coated: 350 - 700 nm (focal length 0.3011 m). https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6508