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Message ID: 116     Entry time: Tue Sep 20 15:34:00 2016
Author: Gabriele 
Type: Optics 
Category: Daily Progress 
Subject: Improved optical lever layout 

Goal

Improve the optical setup, by increasing the response of the QPD to disk motion.

The old configuration

In all my previous measurement the optical lever was as simple as possible: no lenses were used, and therefore the beam was free to expand over all its path. The estimated arm lever from the disk to the QPD was 1030 mm.

QPD response to disk angular motion

The response of the QPD can be characterized with its optical gain in 1/rad, which is how much the normalized signal (difference / sum) changes for one radians of motion of the disk. This is the product of two parts:

  1. the gain from angular motion of the disk to beam spot motion on the QPD. In the simple case of free propagation this is 2L, where L is the distance from the disk to the QPD, and the factor 2 is due to the fact that the beam deflection is the double of the disk angular motion. If there is a telescope in between the disk and the QPD, it is easy to compute the total ray transfer matrix:
    \begin{pmatrix} x_{QPD}\\ \theta_{QPD} \end{pmatrix}= \begin{bmatrix} A & B\\ C & D \end{bmatrix} \begin{pmatrix} 0\\ 2\theta_{disk} \end{pmatrix}
    Then the gain is simply the B element of the matrix.
  2. the response of the QPD normalized signal to beam motion. This depends only on the beam spot radius w on the QPD. It can be computed by simple gaussian integration, and in the approximation of small beam motion, it is given by the following expression:
    g = \frac{2}{w}\sqrt{\frac{2}{\pi}}

In the case of the old configuration, the beam spot size on the QPD was measured to be about 1.5 mm in radius, so the optical gain is of the order of 1900 /rad.

Laser beam profiling

Since I wanted to improve the optical setup, I first needed to measure the beam coming out of the HeNe laser. I used the WinCam beam profile and a Newport rail to measure the beam X and Y sizes at different positions.

The measurements are not the best ever, but I can still get a fit for the evolution of the gaussian beam, as shown in the plot below. The beam waist is 254 um, located 340 mm behind the laser output (inside the laser tube).

Design of the improved setup

I decided to try a brute force algorithmic optimization for the optical gain. I allow two lenses between the laser and the disk and two lenses between the disk and the QPD. I wrote a MATLAB script that picks the four lenses from a list of all those available (I have a Thorlabs LSB02-A lens kit). For each combination of lenses, MATLAB moves them around into pre-defined ranges, and try to find the maximum value of the QPD total optical gain, which is the product of the factor g above and of the B element of the ray tracing matrix.

It turned out that the best optical gains could almost always be obtained by making the beam huge on the disk (5-10 mm radius) and tiny on the QPD (tens of microns). This is not a good solution. So I decided that the beam on the disk must be smaller than 2mm in radius and the beam on the QPD must be larger than 200 microns. I enforced those limits into the optimization code by weighting the gain with a function which is one in the allowed range, and then quickly drops to zero when either of the beam sizes fall out of the allowed range.

The script ran for about half hour and gave me a lot of possible options. After some inspections, I decided to use the following one, which uses only one lens between laser and disk, and two between the disk and the QPD. Distances and focal lengths are shown below. Note that the first distance (laser to first lens) is from the laser beam waist to the lens, so the actual distance must take into account that the waist is estimated to be 340mm into the laser.

With this configuration the optical gain is computed to be 17000 /rad, or about 9 times larger than the original setup. The beam radius on the disk is 1 mm and on the QPD is 0.23 mm.

Implementation

First of all I measured some distances:

  • from the inner side of the viewport to the disk: 420 mm
  • viewport thickness: 12 mm, which is about 18 mm optical length considering n~1.5
  • so from the input to the chamber to the disk: 438 mm
  • from the viewport to the upper external periscope mirror center: 110 mm
  • distance between the periscope mirror centers: 275 mm

Using these distanced I build the designed optical setup. Some remarks on the procedure

  • I first aligned the laser beam to be horizontal, then added the first lens and centered it by ensuring no beam shift far away from the lens
  • I first aligned the periscope to get the beam roughly centered on the inner 45 degrees mirror, and then roughly centered on the black glass
  • Then I put a small container with water inside the chamber, on top of the black glass. I aligned the inner mirror and the periscope so that the beam coming back from the horizontal water surface was perfectly overlapped with the input beam. I used an iris on the input beam path
  • Then I removed the water container and installed a test disk. I moved the disk around until I got the same beam position in output. This tells me that the disk is horizontal
  • Finally I moved the upper periscope mirror to separate horizontally the beam coming back, at the level of the table. The separation is large enough to allow me to pick up the outgoing beam with a mirror.

Here's a picture of the setup, with the optical path highlighted. 

 

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