PALM 3000 – High-order Wavefront Sensor–Design Review

June 2nd 2008, Christoph Baranec

Introduction

This is a draft of the optical design of the high-order wavefront sensor for PALM-3000.

System assumptions

From and HOWFS draft requirements document.

Design wavelengths:Optimized for 400-900 nm, transmission out to 1 um.

Plate scale at focus: 390 µm / arc second.

F/#: 15.77 ± 0.8% (To be appended to the optical bench requirements)

Pupil misregistration <5% of finest subaperture - (P3K-IRD-0405) - discussion in collimator section

Layout

Overall optical length is 16” – vs. 10” is current PALM-AO WFS.

Expected spot sizes

The expected Shack-Hartmann spot sizes in each of the four pupil sampling modes are presented in the table below. These assume an r0 = 9.2 cm (at λ=500 nm) at a declination angle of 30°. The spot sizes include effects from diffraction, aberrations in the wavefront sensor (~0.25”), and charge diffusion (~0.5 pixels).

Pupil / Spot Sizes (arc sec)
(s) / NGS / LGS / Planets
64 / 1.8-2.3*
32 / 1.50 / 2.14 / (3.5/2.7)
16 / 1.33 / 2.04
8 / 1.28 / 2.01

*According to Rich’s error budget tool, rms residual wavefront error only changes by a few nm by selecting a plate scale within this range.

Desired plate scales

The selected plate scales for each sampling mode are presented below with justification following.

64: 2.1”/pix 32: 1.5”/pix 16: 1.3”/pix 8: 0.65”/pix

64x: This sampling is constrained by having a maximum subaperture of 2 x 2 pixels. Therefore the ratio of pixel to spot size (p) should be 1.0 – 1.5 to give good linearity around the zero-point (Hardy table 5.3). With a large tolerance on the effective spot size, the plate scale is selected to be 2.1” ± 0.2” per pixel.

32x: This sampling mode must accommodate NGS, LGS and extended sources for guiding, and has 4 x 4 pixels per subaperture. 1.5” / pixel gives good linearity for the NGS using just the central 4 pixels. For the LGS, p = 0.7 using 2 x 2 pixels mode or using 4 x 4 pixels with a center of mass (COM) algorithm, or p = 1.4 using binned pixels. Guiding on planets can also be done unbinned, where p = 0.43 and 0.56 for Uranus and Neptune respectively using COM or a correlation tracker, or can be done with binned pixels with p = 1.17 and 0.9.*The best centroiding method for the LGS and planets may have to be empirically determined.

16x:This mode makes a slight compromise for NGS over LGS performance. At 1.33” / pixel, p = 1 for the NGS using just 2 x 2 pixels. The LGS requires 4 x 4 pixels whereby in binned mode, p = 1.3, or in unbinned mode, p = 0.65.

8x:Since this mode will be primarily be used for faint NGStargets, a reduction of the effects of read noise and dark current are necessary. Unfortunately the design of the relay requires a limit on the F/# of to be ~> 20. Ideally we would want p = 1, but with the current relay gives spots which have a geometrical size of 38 um (see final performance for image quality). If we instead use the plate scale of 0.65”/pixel, we can bin 2 x 2 and get p = 1.0 at the cost of 4 times the dark current. The relay in this case produces a geometrical spot size of 21 um (10 um rms) due to the increased lenslet array F/#.

Even though linearity is mentioned as criteria for good plate scales, an optional linearization correction in the form of a look-up table will be included in the centroid algorithm design of the real time reconstructor.

Field Stop

We will be attempting to use the same spatial filter that will be fitted to PALM-AO. This requires a maximum opening of 4 arc seconds (1.56 mm) for guiding on solar system objects, and a minimum size of λ/d for 16x sampling (0.48 arc seconds; 190 µm). The spatial filter will only be used as a field stop in the 8x mode since aliasing error will not be the dominant term. More information on the spatial filter can be found at:

Collimator

Desired fl ~ 150 mm – Protected silver coating (on this and fold flat)

  • ‘Best’ design – OAP
  • Field curvature (sag of pupil) = 0.5 mm at edge of pupil
  • Minimum Distortion (pupil magnification - stretch error) = 0.12 % at edge of pupil
  • Mirror can be tilted to introduce pupil elipticity
  • Pupil size error = <0.1 um in x,y
  • No chromatic error
  • Concave spherical mirror at 8 degrees
  • Pupil size will be 63um larger in one direction (total size = 9.664 mm, 184 um = 122% of a x64 subaperture)
  • Field Curvature x = 1 mm, y = 50 nm
  • < 13 nm of Astigmatism added to largest subapertures
  • Might be worth purchasing one for testing or alignment before OAP arrives.
  • Stock achromat
  • Field curvature = 0.2 mm at edge of pupil
  • Distortion = 0.15 % um at edge of pupil
  • Pupil size error:
  • 425-725 nm: +0/-6% of a 64x subaperture
  • 400-900 nm: +6/-6% of a 64x subaperture
  • Partially optimized achromat with air spaced MgF2 singlet
  • Pupil size error:
  • 400-900 nm: +1/-1% of a 64x subaperture
  • Distortion =0.23 % um at edge of pupil
  • Field curvature = 1.4 mm

Pupil z location – Approximately 1 f away, optical bench will reimage exit pupil to inifinity.

Discussion on requirement: Pupil misregistration <5% of finest subaperture (P3K-IRD-0405)

This requirement refers to the actuator-to-lenslet registration. While the absolute calibration may be allowed to be up to 10-15%, the 5% should be a stability to be maintained over an hour long exposure. However, I believe that the 5% spec can be met in an absolute sense as detailed below.

Currently, the angle of incidence on the PALM-AO DM is 7.6 degrees. This causes the footprint on the DM to be elliptical with a major to minor axis ratio of ~1.01. If we indeed want to match the actuator-to-lenslet to a given percentage, we can create an elliptical pupil by either using the spherical mirror or slightly tilting the OAP. Tilting an OAP by ~2 degrees matches the elipticity of the pupil on the current DM. The advantage of using an OAP is that the pupil can be made circular or eliptical, while due to packaging constraints, the spherical mirror will have a minimum projected pupil elipticity of 1.02. This correspondes to an AOI on the DM of 11.5 degrees.

Drawbacks to using astigmatism to add pupil elipticity: added astigmatism of 300 nm RMS astigmatism in the WFS. This corresponds roughly to the edge subapertures run off null by 2 um over a 2x2 (48x48 um^2) subaperture. *This can be compensated in two ways. A cylindrical lens located near the lenslet array which can correct for all of the astigmatism. Alternatively, the first relay element can be tilted and decentered to compensate for astigmatism at one of the sampling modes. The others are only partially compensated as the lenslet array focus changes.

Added astigmatism to WFS by matching elipticity of pupil on DM with AOI of 11.5 degrees

Proposed strategy: Since the only real advantage of using an OAP is creating a spherical pupil, and there is uncertainty in the final F/# of the OAP relay leading to uncertainty on collimator focal length (and is on the order of 7-9K), I propose that we instead build the system with a spherical collimator. I suggest that we first use an off the shelf part ($300) and once we have the full system built up in the lab, we can use the beam profiling camera to check the beam size. If we need to get another collimator that has a slightly different focal length, then we order it at that time. A custom ½” mirror with a tolerance on the focal length of 0.1% (to match 5% registration in size) will be around $XX. This way we can be absolutely sure of the pupil size, as well as match the geometry of actuators to lenslet array. The drawbacks are that the angle of incidence on the DMs will have to be a minimum of 11.5 degrees, and there is 300nm of astigmatism in the WFS (which can be corrected with an additional element, or partially corrected by tilting/decentering the relay lens).

collimator / Spherical / OAP / Tilted OAP / Triplet Lens
Lenslet Pupil Geometry / Matched to DM / Circular / Matched to DM / Circular
Static Errors / ~300nm Astig* / - / ~300nm Astig* / -
Cost / $300 + $XXX / $7-9K / $7-9K / $5K (?)
Lead time / 1wk + XX wk / 5-6, 8-10 wk / 5-6, 8-10 wk / 8 wk (?)
Throughput / Two Reflections (1) protect. Ag (2) super mirror (99.9%) / Same sphere / Same sphere / 4 air-glass interfaces
Additional / AOI on DM >11.5 degrees / Lower throughput
Additional (2) / Final part can be manufactured / Tight tolerance on system F/# must be observed
quickly to match system F/#

We need to make a decision soon as to the collimator choice.

Final pupil registration will need to be done in lab in closed loop.

Lenslet arrays

Based on desired plate scales listed above, we want the following lenslet arrays for use with a 150 mm focal length collimating lens:

m / D / name / s / d (mm) / f (mm) / Roc (mm) / Sag (mm) / F/#
0.318 / 9.664 / 1 / 64 / 0.151 / 14.05 / 6.3206 / 0.0005 / 93.02
0.318 / 9.664 / 2 / 32 / 0.302 / 19.66 / 8.8488 / 0.0013 / 65.11
0.318 / 9.664 / 3 / 16 / 0.604 / 22.69 / 10.21 / 0.0045 / 37.56
0.318 / 9.664 / 4 / 8 / 1.208 / 45.38 / 20.42 / 0.0089 / 37.56

Ideally all four would be made on the same substrate with an ‘active area’ of 24.16 x 24.16 mm (an extra subaperture in every direction with the s = 8). Will be AR broadband coated on both the front and back.

Relay system

Design consists of two stock lenses, LAL017 and LAL007. Each have broadband AR coating from 400-700 nm stock.

m = 0.31788

Can be used at magnifications ±10% with negligible decrease in image quality. Can be used at m±20% with image size increase of 20%.

Figure below shows the spots from an F/37 beam at the center and edge of the lenslet array. Slower F/#’s have smaller spots.

Extremely low distortion: <0.002% or <0.3 um at edge.

Performance of entire system:

Spots sizes: (each pixel is 24 um)

64x: 9 x 9 um geo spot size – 4.6 rms diffraction limited

32x: 13 x 13 um geo spot size, rms 5.1 um

16x: 18 um x 18 um geo spot size, rms = 9 um

8x: 21 um x 21 um geo spot size,rms 10 um (38 x 38 um [rms 20] if 1.3”/pixel)

RMS spot size typically 0.5x geometric size from relay design. Lambda weighted QE of system will reduce RMS spot size further.

Testing notes

Will need access to interferometer / wavefront sensor to confirm manufacturer’s specs on collimator.

Now have small pixel, large format camera for alignment collimation testing (Pixelink PL-B781F, 3.5um pixels 3000 x 2208)

Atmospheric dispersion corrector (ADC)

It is not clear that we absolutely need an ADC in the system, however we will leave room to add one later if necessary. A space has been chosen between the fold mirror and lenslet array, in collimated space, where there is 47 mm of space, not accounting for the collimator or lenslet array mounts. A rotation stage (ex. Newport PR/SR50, 21 mm total depth) can be placed into this area. When using the laser guide star, we would want to move the ADC out of the beam path to reduce transmission losses.

The ADC will reduce the spectral elongation of Shack-Hartmann spots on the detector. In its proposed location, the incoming image in the WFS will still be elongated before it enters the spatial filter.

Additionally, Brian Bauman comments that GPI is using an ADC and that this distorts the WFS pupil by 0.2%. There is no anamorphic prism pair to correct for this; they will be using modal control with a Fourier basis set.

Motion control

Focus control will be provided by the current PALM-AO Aerotech ATS100 stage.

The sensor will require 3 additional linear stages, two for switching/positioning of the lenslet arrays, and one to refocus the relay/detector assembly.

The lenslet array stages will require a minimum of 12 mm travel and precision of < 5 um and a small form factor. A recommendation would be Newport MFA-CC miniature linear stage: 25 mm travel, typical < 4 um repeatability from home position, 0.8 x 5.5 x 1.77 inches. ($1.6k ea).

The relay/detector assembly requires a minimum of 31 mm of travel, position repeatability of ~10 um. For reference, .1 arcsecond of motion (3.5 um at the lenslet focal plane) corresponds roughly to 35 microradians of pitch flexure of the relay/detector assembly. Suggested Newport ILS50CCL (~$3K) which has a pitch spec of 40 microradians, travel of 50 mm and 0.5um resolution.

Controller solutions will be in consultation with John Cromer. Suggested Newport 4x SMC100CC ($800 ea)

Cooling

The camera head will be cooled, and will be tested in the lab under different cooling conditions. This is mainly an issue when guiding on faint NGS, when running in x8 sampling mode when by necessity each subaperture must use 16 pixels. Cooling solutions include a passive radiator, flexible heat pipe to the breadboard, liquid cooling to a heat exchanger outside of the top box enclosure, and if necessary, liquid cooling provided by Palomar to the Cass cage.

Budget
System / Type Part / Part
Optics / Collimator / Test Sphere (CVI) / $300
Custom sphere / $2000 (?)
OAP / $7000-$9000
Triplet / $5000 (?)
Flat / Thorlabs bb05-e02 / $51
Lenslet array / MEMS / $42,200
Relay 1 / MG LAL417 / $144
Relay 2 / MG LAL407 / $85
Astigmatism corrector / Custom / $(?)
Spatial Filter / From PALM-AO / -
Mounts / 2 Mirror mounts / $170
2 Lens mounts / ~$200
Lenslet array mount / Custom CIT
L.A. stage interface / Custom CIT
Relay/Detector interface / Custom CIT
WFS breadboard / Custom CIT
Stages / Lenslet positioner / Newport MFA-PP / $2,800
Detector focus / Newport ILS50CCL / $3,000
Controllers / As needed SMC100 / $3,600
Other
Total / Sphere option / $54,850+
OAP option / $60,850+

Quotes: (for reference)

OAP:

SORL $7,825 (4-6 weeks or 14-16 weeks)

B-Con 2x for $6420 (5-6 weeks) Aluminium

Nu-Tek $14,800 (12-13 weeks) for custom; stock f=146.6mm Zerodur $8750. (8-10 weeks)

No-bid: HJOL, Optiforms, JR Cumberland

Still waiting: Optics Technology

Lenslet arrays:

Wavefront Sciences – can’t meet sag requirement

MEMS Optical – $42,200 (10-12 weeks)

SUSS MicroOptics – e50,000 ($77,725) no eta

Vitrum – Hard to stay in continual contact – Approximately $10,000.