Filter cavity 775 mode matching

[Torrey,Jeff]

Update to 11463. One of the lens was definitely bumped in the 3 months since this post. Jeff and I remeasured the beam profile and adjusted the MM solution accordingly. Attached is the most up to date profile of the beam and beam parameters calculated via 11292. We then used JAMMT to account for the curvature of the optic that the beam will initially pass through. jammt_model_775.png calculates a beam waist of 443 um at 2.75 accounting for a plano concave mirror with a radius of curvature of -1.6m and index of refraction of the material of 1.444. Finesse predicts <1% cavity mismatch for these parameters.

If anyone wants to calculate this themselves the following distances between the optics are up to date, where the collimator is 0. Additionally the distances for a half trip through the cavity are done from Daniel's (x,y) coordinates of the mirrors in the filter cavity. These values are (11.779,1.163). This means the distance of a half trip in meters is d = [sqrt(11.779^2 +1.163^2)*2 + 11.779*2] * .0254 = 1.2 m. Add this on to the distance from the collimator Cavity M3 is to get the approximate waist location required in the cavity (should be at the M1 position, as seen in labpic_w_labels.png).

	Distance (Inches)	Distance (m)
775:M1	12	0.3048
775:M2	16	0.4064
775:M3	46	1.1684
775:M4	50	1.2700
Cav M3	61	1.5494

 

End Mirror Wavefront Correction Data and Analysis

To decide whether the end mirror should be circular up to the spoke "full ring" or whether there should be a flatter interface "cut ring", I simulated both in COMSOL with 2 mode corrections, the 20 + 02 HG mode and the 11 HG mode.

In summary, the rounder optic seems to perform a bit better when considering the deformation per joint stress, deformation per force applied, and eigenfrequency. The more circular mirror also has a cleaner edge and a larger reflecting surface. If Knight Optical can make them, I think we should get a circular mirror.

Full ring:

20+02,60 N:

9 MPa Max stress

6.3 mD adjustment

0.7 mD/MPa

0.1 mD/N

 

11, 25 N:

4.3 MPa Max stress

9.4 mD adjustment

2.2 mD/MPa

0.37 mD/N

 

 

Resonance: 3943 kHz

 

 

Cut ring:

20+02, 60 N:

8 MPa Max stress

4.2 mD adjustment

0.52 mD/MPa

0.07 mD/N

 

11, 25 N:

3.6 MPa Max stress

8.6 mD adjustment

2.4 mD/MPa

0.34 mD/N

 

Resonance: 3878 kHz

Output filter cavity high reflectivity optics installation

[Torrey, Ian, Jeff]

Cavity super optic sn s2400001 part # m2, a flat HR 775 1% 1550 0ppm.

Part m2 serial number 16 is being opened and is going to the m3 slot. The orientation of the labels on the mirrors and how it looks on the optics table is flipped. When looking at the cavity on the optics table, we've been calling M3 the bottom left mirror. This is actually the part labelled M2. See this for labelled picture.

https://wiki.mccullerlab.com/DCC/S2400001 has been updated accordingly.

 

High laser power

[Torrey, Jeff]

Because the SHG is inefficient at low powers, the amplifier needs to be turned on to achieve sufficient 775 nm light power. The following power measurements were taken upon turning up the amplifier pump current (currently 1 amp):

Input on SHG sled going to OFC: 1.92 mW (775)

Output on OFC sled: 1.38 mW (775) and 36 mW (1550)

input to filter cavity table: 36 mW (1550)

high power path (MISC): 342 mW (1550)

Note: Can't measure directly in front of the SHG input without blocking it and disrupting it. MISC path is measured instead which should be close to identical. Adding up the four paths plus a 5% total loss before these measurements gives roughly 800 mW total out of the amplifier at the moment.This may be increased in the future.

 

piezo alignment/centering tools

[Torrey, Daniel]

The alignment tools for centering the piezo on the mirror for the output filter cavities are in the global industrial cabinet above the label PIEZO ALIGNMENT TOOL. I tested out daniel's latest version for the large thorlabs piezo and it works well. I did not achieve a robust lock with this piezo. I suspect this more has to do with poor alignment on the REFL PD used for PDH locking as the error emplitude is much smaller in this configuration even with the tank circuit boost to the phase modulations. The error signal is clean but the amplitude is only 1.7 mVpp on 0dB input gain vs other piezos that reached as high as 12 mVpp on similar gain settings.

More time could be spent on this but I am transitioning to cavity super optics and 775 nm light today. 

Buzz good controllers

wield-control sha 82d56d463393e5b1176c22104f336b6db36f93e9 and buzz sha f4e584ab29cd93098789189d5acbf6f421bcec7b do recover the good set of controllers.

The current setup for some reason does not recover them, so this gives a recovery checkpoint.

SWIR camera is overheating

The SWIR camera in B102 is overheating. The temperature was measured at 130 F. We have temporarily unplugged it over the weekend until we can investigate. We think the PLA 3D print that is mounting the camera may be contributing.

Script to save filter in the form the moku requires

[Jeff,Torrey]

For anyone trying to upload some filters to the moku, here is a short python notebook to do so.

GQuEST cavity optics in B102

The filter cavity optics are in a drawer of B102. Please log and update when any of these optics are moved. Log changes in this log, and update the whereabouts on the wiki page:

https://wiki.mccullerlab.com/DCC/S2400001

These are tied to the DCC number as well (it will just link back, but the original spec was pulled from a LIGO DCC number):

https://dcc.ligo.org/LIGO-T2300191

Attached is an image where the optics are.

As you remove the existing cavity optics, the M1 of the cavity is a prior version of these. Please update also with the whereabouts of those 4 optics (They could be M0 or something).

Adding an inductor to the EOM for filter cavities

[Torrey, Ian]

We added a variable inductor in series with the EOM to make a resonant LC circuit (tank circuit as Lee called it) to boost the phase modulation used in the PDH locking of the filter cavity. This should increase the modulation depth at the frequency f = 1/(2*pi*sqrt(LC)). The EOM capacitance can be found on the thorlabs website with a value of 14pF. Solving this equation for our current modulation frequency gives roughly 700 nH inductance required. We have a box of variable inductors in the lab. We put one of these in and tuned the inductance to maximize the error amplitude. This gave a 3x boost to the error amplitude, while the loop still provided the same amount of supression. This gives a ratio of the error amplitude to RMS of the cavity lock of 230mV/14 mV of ~16. This should be sufficient now to swap out to the good diachroic mirrors.

Control discusssion from Alan and Ryan

I'm copying here questions that Alan and Ryan sent about precision and implementation.

In order to better estimate FPGA resources, which will likely impact latency, it would be useful to know how many bits are the a and b coefficients (in the direct form I). 

Can you say the expected resolution of the a and b coefficients? 

Also, can we assume the filter is 2nd order? Or if not, what values are needed for M and N?

I am thinking we can assume x is 16b and y is 16bits for this first analysis? 

Ryan has produced a Verilog model of a digital filter based on the depiction of a direct form I implementation as illustrated in the link you provided.

 

There are a couple of possibilities to consider. One is that a digital filter model of the controller in a feedback arrangement is to be generated. For example, in the block diagram below:

 

 

The controller could be represented by the block labeled as C(z) intended to reflect the Z transform representation of the controller. The “plant” (represented by P(z)) is the entity that it is desired to control. F(z) represents the feedback mechanism (which may have dynamical behavior of its own) and it is assumed that the implementation is designed to provide negative feedback.

 

As you can see from the system transfer function, H(z), there can be poles of the system (zeros of the denominator of the system transfer function) that must be considered to be sure that the system is stable under the presence of all inputs, x(n).

 

Question: Is the direct form I model that we are developing the entire H(z) model or just the C(z) (controller model)?

 

If the difference equation (from which the direct form I model is derived) is representative of the entire system then knowledge of the coefficients a(1), a(2), …, a(M) is all that is needed to investigate the poles and their locations relative to the unit circle (from which the stability can immediately be determined, ignoring for a moment the effects of finite-precision arithmetic).

 

If, on the other hand, the full model is not represented by Ryan’s code, we will need to have more details (say the transfer functions P(z) and F(z) or their time domain representation equivalents) to be able to capture the behavior of the entire loop.

 

control system reference links

For reference, here are links about digital filters:

 

Chris Wipf implementations:

Perform IIR filtering sample by sample on TYPE (float/double/long double). /// Implements cascaded direct form II second order sections.

https://git.ligo.org/-/snippets/137

 

Python implementations of second order sections filtering (scipy.signal)

https://github.com/scipy/scipy/blob/v1.13.0/scipy/signal/_signaltools.py#L4245-L4354

 

Transposed direct form 2 Direct form II of this Wikipedia page: 

https://en.wikipedia.org/wiki/Digital_biquad_filter

 

https://github.com/scipy/scipy/blob/v1.13.0/scipy/signal/_sosfilt.pyx

 

sosfilt.py line 75 has the comment “Use direct II transposed structure”

Measurement of 1-inch blank silicon substrate fron Knight Optical

Daniel and I measured the diameter of one of the 1-inch silicon substrates from Knight Optical, which are intended to be coated to be end mirrors. See attached photos.

We used calipers to measure the diameter along two roughly orthogonal directions, and found it equal to 1.0005 inches for both. 

Piezo Alignment Tool

[Torrey, Daniel]

Torrey thinks that the central axes of the piezo and the mirror are misaligned. I designed a part that aligns the small piezo and a 1/4 in thick spacer with a #8 through hole with the "piezo top". This piezo top should be well aligned with the piezo bottom that holds the mirror. I believe this should give alignment of the axes to within ~5 thou rms (3 thou from the piezo top to the base, 4 thou from the mirror in the SM1 threads, and ~1 thou from this tool).

Attached is the part file with CAM as well. I decided to make this part in a CNC Lathe for its precision compared to a 3D print. An important consideration is the radius of curvature of the cutting tool. This is why there is a notch toward the thickest part of the tool and why the levels of the tool don't match the levels of each part. If one were to 3D print this part, they should remove the notch so that there are no overhung sections.

The blue colored photo is the CAM simulation.

Filter Cavity Piezo Mirror Alignment

[Daniel, Torrey]

The theory from post 11547 was that the centering of the piezo on the back of the mirror in the cavity was improved (accidentally) between swapping them out while Masayuki visited the lab. This potentially improved the quality of lock drastically. Because the small thorlabs piezo has proved the best in the cavity, we need a way to repeatedly align the piezo in the center of the back of the mirror. However, Daniel's compression design to hold the piezo in place was not designed for a piezo so small. To combat this Daniel has machined a part will help align the small thorlabs piezo in the piezo compression set up. See 5ED5222C-108A-401E-993C-77349E63ED9C.jpg. The skiniest cylinder on this piece is the same as the inner diameter as the small thorlabs piezo. 

Additionally, we noticed that the spacer being used in the piezo assembly was one with an inner diameter for a 1/4-20 screw. This is close to the size of the outer diameter of the small piezo. We swapped out this spacer to one with a smaller inner diameter so the piezo has more to rest on. With the previous spacer the piezo didn't have a full, flat surface to rest on. Alignment hasn't been recovered, update on the effects of centering/new spacer to follow.

Filter cavity and (more) optimal controls

[Jeff, Ian, Torrey]

With results from 11547 and 11541, we have a calibrated spectrum in m/sqrt(Hz) of the filter cavity. From this calibrated noise spectrum the goal now is design a controller that minimizes the noise when multiplying by the closed loop gain. However, after playing with the moku alot there are a few caviots. 

1) Ideally we would upload a custom filter with the desired shape into the low pass filter in the laser lock box. However, the moku requires a text file with the filter described in second order sections (SOS). Most places that you can upload a filter allow up to four rows of SOS to describe your controller. For some reason at only this low pass filter in the laser lock box, it only allows less than 3 (haven't tried 2 rows, but doesn't except 3). This allows us potentially with 4 poles and zeros to describe your optimal filter, which is not ideal.

2) The second idea was to upload the full controller in the digital filter box (DFB) where the summing of the excitation signal is used when taking transfer functions. The problem with this is it saturates the scan signal and therefore the output going to the piezo, meaning we can't actuate on the length of cavity. It seems two things saturate this signal: having any amount of gain at DC in the controller and having a positive gain near the resonant frequency, which at the time of this experiment was 8.25 kHz (this may have changed, see future log post). Both of these are problematic, but not being able to have any gain at low frequencies makes this not useable.

In order to get around this, I split the controller up into two parts. The first part is in the fast controller of the lock box, and the second is a filter still uploaded to the DFB, but taking into account that there is some shaping in the laser lock box. So now what this looks like is, we use previous results to design a (more) optimal controller, divide out the shape of the fast controller to get the shape that should be uploaded into the DFB. The idea being that one can lock the cavity with just the laser lock box and then turn on the custom DFB filter as a noise eater, to further improve the quality of lock.

So, for example, if we thought optimalshape.png was our optimal controller, we can find the filter that when doing Fast_Controller * mystery_filter = optimal_shape. optimalproduct.png shows roughly what this looked like. Converting this to SOS and uploading to the moku using Jeff's code makes the cavity lock much worse.  My best guess at the moment is that there is a flaw in our understanding of the actual noise in the system, leading to a controller that isn't supressing at the correct frequencies. More investigation is needed.