Shack-Hartmann imager

Jan 10, 2022

We can construct a Shack-Hartmann imager for the second Nasmyth port on Aux Tel, to serve as a diagnostic tool and ground-truth calibrator for dome seeing diagnostics. 
The basic principle is described here: https://en.wikipedia.org/wiki/Shack%E2%80%93Hartmann_wavefront_sensor from which this figure is taken:

We can use the Sony high frame rate camera and a lenslet array to do this. Positioning the lenslet array a distance D from the focal surface of the telescope produces (for a single bright star) a donut image of diameter D/18, since the beam is converging at f/18. For this to fill a 10mm x 10mm lenslet array, we would need to position the lenslet array 180mm = 18 cm = 7 inches from the focus. Note this can be behind the focal surface if need be. An angular displacement of 1 arcsec would produce a centroid displacement at the image made by one lenslet of 4.86E-6 * MLFL where MLFL is microlens focal length. For a long microlens focal length of around 40mm we would see 0.2 microns of image displacement. 

The coherence time for wavefront perturbations is a few msec so we need a frame rate approaching 1 kHz if possible. 

Spatial sampling of the pupil depends on the lenslet configuration and size of donut that lands on the array. A 10mm x 10mm lenslet array with 500 micron pitch would give us a 20 x 20 sampling of the pupil, or a spatial resolution of about 6 cm x 6 cm at the pupil. That is plenty good enough. 

We have some options for the camera we use. 

1) Sony DSLR: Since the Sony camera has a built-in lens and a 35mm focal plane with 2.4 micron pixels, we want to re-image the spots behind the lenslet array onto the sensor. This means we need to use a macro lens configuration, ideally with some magnification. 

2) We could just put a fast monochrome CMOS camera about 45mm behind the lenslet array and make a 10mm x 10mm image onto that, directly. 

Potential devices:

Sony RX-10 camera: 

13.2 x 8.8 mm sensor, backside illuminated CMOS, 2.4 micron pixels 

review: https://www.dpreview.com/reviews/sony-cybershot-dsc-rx10/2 

close-up Macro lens: https://www.amazon.com/Cyber-Shot-DSC-RX10-Element-Close-Up-Diopter/dp/B07L6ZVWBY 

The Sony camera claims ability to take a burst of 1000 frames per sec for 912 x 308 pixel subarray. See http://www.hispeedcams.com/sony-rx10-iv-improves-hfr-resolution/ for example

It seems minimum focus distance to object with no macro lens attachment is 3 cm when lens is set to 24mm focal length. See https://whiteknightpress.com/sony-rx10-iv-minimum-focus-distance/ 

From https://helpguide.sony.net/dsc/1720/v1/en/contents/TP0001582249.html :

Good reference for the Sony RX10 IV camera: https://www.kenrockwell.com/sony/rx10-iv.htm

Camera manual: 47257441M.pdf

Rough estimate of magnification is 0.8 which means microlens array of spots is about 8mm x 8mm which basically fills the sensor. 

The sony camera takes 72mm filter threads, at thread pitch of 0.75mm, on the front of the lens. Thor labs sells adapters from metric threads to their SM1 and SM2 lens tube standard, but only up to 54mm diameter. See https://www.thorlabs.com/navigation.cfm?guide_id=2327. 

We can use a step-down filter adapter ring to do: 

72mm external threads to 52mm internal threads, using adapter rings for photography filters. Example: https://www.amazon.com/Adapter-Connection-Accessory-Cleaning-72mm-52mm/dp/B0986NSTNL/ref=sr_1_3?crid=2RN0RACZH9P1M&keywords=72%2Bto%2B52mm%2Bring&qid=1641874030&s=electronics&sprefix=72%2Bto%2B52mm%2Bring%2Celectronics%2C111&sr=1-3&th=1

Thor Labs SM2A53 will give us external 52mm threads to match that, so SM2 components can be bolted directly onto Sony camera. 

I ordered both of these adapters on Jan 10, 2022. 

Also bought three mounted Thor Labs microlens arrays: 

Software:

An alternative approach: 

(Jan 11, 2022)

Imagine using a lens or mirror to generate a collimated beam at the focus of Aux Tel. The optical invariant of etendue is the A-Omega product of the beam area and its angular divergence. If at the 1.2 meter entrance pupil the rays span a range of 1 arcsecond, then if we make a collimated beam of diameter 10 mm the angular magnification is a factor of 1.2m/10mm = 1,200 mm/10mm = 120. An angular deviation of 1 arcsecond at the input then produces a spot displacement on a Shack-Hartmann sensor of 4.86E-6 * 120 * (microlens focal length) = 5.8E-4 * focal length = 11 microns per arcsec * (FL/20mm). 

Since image is about 1200 x 1200 pixels, we should be able to monitor about 1/4 of it at 1000 frames per sec (see Sony table above) for a burst of data collection lasting a few seconds. 

Larger lenslet arrays: 

A larger lenslet array would increase the acceptance of the system, and be more forgiving to pointing and tracking issues. RPC photonics makes bigger ones, have asked for quote on 1/12/22:
"Hi. I'd like a price and delivery quote for MLA-S250-f30 in the 50.8 x 50.8mm size, qty 2, please." 

Biggest Thor labs lenslet pitch is 300 microns. Edmund sells a 10mm x 10mm microlens with 500 micron pitch. What does that correspond to in pupil plane? Dx=(1.2m/8mm)*0.5mm = 75mm or 3 inches. 

During image quality meeting on 1/13/22 Brian Stalder told us the external DIMM aperture size is 3 inches diameter and about 8 inch spacing between them. So a 500 micron pitch is a good match to the DIMM aperture. 

So I am going to order Edumnd large-pitch lenslet array, plus mirrors for f/18 beam emulator. 

This coarser lenslet array will give us a ~16 x 16 array of spots for an 8mm dia beam. 
the longer focal length of 46.7mm produces a spot displacement of 3.4 microns * (46.7/5) = 32 microns/arcsec. The full-bayer pixel size on the Sony camera is around 5.5 microns. Even with factor of three de-magnification this gives us a nice 2 pixels across the image size. 

Actually I think the spots might be larger? For one arcsec,  AuxTel makes a spot 100 microns in size (FWHM). The collimator has 152mm focal length, the microlens has 46.7mm focal length, so that means spots are 100 microns * (46.7/152) = 31 microns. Whew.  

This vendor looks good: http://www.okotech.com/microlens-arrays 

Have asked for a quote for 1500 micron pitch in 25.4mm x 25.4mm size. That would give us a factor of (1500/500)^2 = 9X more photons per sec per spot. Separation between spot centroids in the pupil plane is (1500 microns)*(1.2m/8mm) ~ 10 inches. 
So each of these 1500 micron lenslets is like a 10 inch telescope, and we'd get around 200 photons per spot per millisec of integration, for a 0th magnitude star. 

Rough Flux estimate

Each spot in our SH sensor is therefore the equivalent of a 3-inch telescope with 3 reflections off aluminum.  What's the photon rate? 

Vega, a 0th magnitude star, provides around 1000 photons/sec/cm^2 in V band, which is roughly equal to one of the color channels in the camera. We can estimate loss from 3 mirror reflections as 0.85^3=0.6, and detector QE of around 0.7, so net photon throughput is around 0.6*0.7 ~ 0.5. 

If our effective aperture for a lenslet is 7.5 cm, the collecting area is 44 cm^2. So for a 0th mag star we expect a photon rate of 1000 * 0.5 for throughput * 44 for area ~ 22000 photons per second. 

Indeed, for 500 micron lenslets and 1 kHz frame rate, we get 22 photons per spot. Ouch. 

For fast frame rate, an even coarser lenslet array would be useful. Star counts, for Dec < 0 (i.e. Southern hemisphere stars). See http://simbad.u-strasbg.fr/simbad/sim-sam?Criteria=Vmag%3C2+%26+dec+%3C+0&submit=submit+query&OutputMode=LIST&maxObject=10000&CriteriaFile=

Southern star counts

For pickoff-acquisition camera:

We want a small, simple, cheap camera with 20 arcsec FOV and python interface. 

Plate scale is 4.86e-6*18*1.2m per arcsec or ~100 microns per arcsec. That means we need a minimum of 2 mm x 2mm imaging area to get 20 x 20 arcsec FOV. 

Here is a good rundown on python-interfacing camera vendors: https://rk.edu.pl/en/scripting-machine-vision-and-astronomical-cameras-python/ 

Bought ZWO monochrome imager, 12 bit A/D, 
https://astronomy-imaging-camera.com/product/asi174mm-mini-mono 

f/18 beam emulator:

A point source put at the radius of curvature  (not the focus) of a parabolic mirror, slightly off-axis, makes a 1:1 re-imaged spot. Since the location is twice as far from the mirror as the focus, an "f/5 parabolic mirror" used in this mode is going to make an f/10 converging beam.  That's the rationale behind ordered the spherical and parabolic mirrors shown here: 

Rough data rates. 

The Sony camera will record 1244 x 420 pixels at 1000 images per second. Let's assume each color plane has 16 bits (2 bytes) of data, times 3 planes times 1244 x 420 pixels. With no compression gain this would require 
1244x420x2x3 = 3 Megabytes per image. At 1000 frames per second and no compression we will need 3 GBytes per second of imaging. It can't record continuously at this frame rate. Let's assume it's a 50% duty cycle, so that time-averaged data rate is around 1.5 GBytes per second. An 8 hour night will require 1.5 GBytes/sec*3600 sec/hour * 8 hours = 43 TBytes per night if we took images continuously. That's more than LSST!

A 256 GB card would store about 30 bursts of 3 second clips at 1000 frames per second. The maximum write rate on most SD cards is around 300 MB/sec, So duty cycle in data collection (based on 1.5 GB/sec image rate) is more like 0.3/1.5 = 20% so max data per night is more like 0.6 GBytes per second (time-averaged) or around 10 TBytes per night. 

We would need to write data at 1.5 GBytes/sec to keep up. This external SSD will write at 1 GB/sec: 

So.. at $125/TB with manual swapping of disks, it would cost around $5K to equip a computer to store one full night's worth of data. 

Ordered one of these, for testing. 

Found a 1 TB fast-write SD card on Amazon, a no-name vendor but claims V90 speeds of around 300 MB/sec: 

ordred 4 of these. 

Also got super-fast card reader: 

References:

The Shack-Hartmann Wavefront Sensor for the Rubin Observatory Dec 2.pdf