Wavefront Sensing In Other Disciplines 15 February 2003 Jerry Nelson, UCSC Wavefront Congress
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Contents What is purpose of wavefront sensing Probes of wavefront error sources Role of wavefront sensing in adaptive optics Methods of wavefront sensing 15feb03 Nelson wavefront sensing 5
Purposes of wavefront sensing Measure the wavefront error for knowledge Statistics of human visual aberrations Measure the wavefront error for later correction (eye prescription) Measure the wavefront error for system analysis and optical alignment Test optics during fabrication align telescope optics (rigid body) slowly adjust shape of a deformable primary Adjust segmented mirrors (rigid body alignment) Measure the wavefront error for adaptive optics 15feb03 Nelson wavefront sensing 6
Probes of wavefront error sources Need light to pass through disturbed region in order to estimate disturbance Natural light Laser beacons Measurement light may be at different wavelength (if index variations with wavelength are small enough) Light closely follows science path, or Tomographically establish disturbance path error 15feb03 Nelson wavefront sensing 7
Probes of wavefront error sources Error sources are often 3- dimensional Typical wavefront sensing measures line integral through 3D volume When 3D nature of wavefront errors is needed, can use tomography to establish this Useful in astronomy in order to increase the diffraction limited field of view (can study bigger field, more objects) Needed when range of angles of study exceeds isoplanatic angle 15feb03 Nelson wavefront sensing 8 θ
Tomography and Multi-conjugate correction 15feb03 Nelson wavefront sensing 9
Overview of wavefront sensing Measure phase by measuring intensity variations Difference between various wavefront sensor schemes is the way in which phase differences are turned into intensity differences General box diagram: Wavefront sensor Guide star Telescope Optics Detector Reconstructor Turbulence Transforms aberrations into intensity variations 15feb03 Nelson wavefront sensing 10
Methods of wavefront sensing Tomography Integrated Sense in pupil plane Shack-Hartmann sensor Point source centroid Correlation tracking of extended objects Curvature sensing Shearing interferometry Pyramid sensing Point diffraction interferometer Sense near image plane Image sharpening Phase diversity 15feb03 Nelson wavefront sensing 11
How to use intensity to measure phase? Irradiance transport equation (Teague, 1982, JOSA 72, 1199) Let A(x, y,z) = [ I(x, y, z) ] 1/2 exp[ ikφ(x, y, z) ] Follow I(x,y,z) as it propagates along the z axis (paraxial ray approximation: small angle w.r.t. z) I z = I φ I 2 φ Wavefront curvature Wavefront tilt 15feb03 Nelson wavefront sensing 12
How to reconstruct wavefront from measurements of local tilt 15feb03 Nelson wavefront sensing 13
Shack-Hartmann wavefront sensor concept - measure subaperture tilts f CCD CCD 15feb03 Nelson wavefront sensing 14
Example: Hartmann test of one Keck segment (static) Reference flat wavefront Measured wavefront 15feb03 Nelson wavefront sensing 15 Gary Chanan, UCI
Resulting displacement of centroids Definition of centroid x y I(x, y) x dxdy I(x,y)dxdy I(x, y) y dxdy I(x,y)dxdy Each arrow represents an offset proportional to its length 15feb03 Nelson wavefront sensing 16
Quantitative description of Shack- Hartmann operation Relation between displacement of Hartmann spots and slope of wavefront: r k x = M f φ(x, y) where k = 2π/λ, x is the lateral displacement of a subaperture image, M = f telescope / f collimator is the demagnification of the system, f is the focal length of the lenslets 15feb03 Nelson wavefront sensing 17
Example: Keck adaptive optics system Telescope diameter D = 10 m, M = 2800 size of whole lenslet array = 10/2800 m = 3.57 x 10-3 m Lenslet array is approx. 18 x 18 lenslets each lenslet is ~ 200 microns in diameter Sanity check: size of subaperture on telescope mirror = lenslet diameter x magnification = 200 microns x 2800 = 56 cm ~ r 0 for wavelength λ between 1 and 2 microns Now look at scale of pixels on CCD detector: Lenslet array size (200 microns) is larger than size of the CCD detector, so must put a focal reducer lens between the lenslets and the CCD: scale factor 3.15 15feb03 Nelson wavefront sensing 18
Neptune at 1.65 microns Without adaptive optics With adaptive optics 2.3 arc sec May 24, 1999 June 28, 1999 15feb03 Nelson wavefront sensing 19
How to measure distance a spot has moved on CCD? Quad cell formula b δ δ x b (I 2 + I 1 ) (I 3 + I 4 ) 2 (I 1 + I 2 + I 3 + I 4 ) δ y b (I 3 + I 2 ) (I 4 + I 1 ) 2 (I 1 + I 2 + I 3 + I 4 ) 15feb03 Nelson wavefront sensing 20
Disadvantage: gain depends on spot size b which can vary during the night b Slope = 2/b δ x,y = b 2 (difference of I 's) (sum of I 's) 15feb03 Nelson wavefront sensing 21
Another disadvantage: signal becomes nonlinear for large angular deviations b Rollover corresponds to spot being entirely outside of 2 quadrants 15feb03 Nelson wavefront sensing 22
Curvature wavefront sensing F. Roddier, Applied Optics, 27, 1223-1225, 1998 More intense Less intense I + I I + + I 2 φ φ r r r δ R Normal derivative at boundary Laplacian (curvature) 15feb03 Nelson wavefront sensing 23
Wavefront sensor lenslet shapes are different for edge, middle of pupil Example: This is what wavefront tilt (which produces image motion) looks like on a curvature wavefront sensor Constant I on inside Excess I on right edge Deficit on left edge Lenslet array 15feb03 Nelson wavefront sensing 24
Simulation of curvature sensor response Wavefront: pure tilt Curvature sensor signal 15feb03 Nelson wavefront sensing 25 G. Chanan
Curvature sensor signal for astigmatism 15feb03 Nelson wavefront sensing 26
Third order spherical aberration 15feb03 Nelson wavefront sensing 27
Practical implementation of curvature sensing More intense Less intense Use oscillating membrane mirror (2 khz!) to vibrate rapidly between I + and I - extrafocal positions Measure intensity in each subaperture with an avalanche photodiode (only need one per subaperture!) Detects individual photons, no read noise, QE ~ 60% Can read out very fast with no noise penalty 15feb03 Nelson wavefront sensing 28
Status of AO systems today Curvature systems: modest no. of degrees of freedom (dof) Canada France Hawaii Telescope: 13 dof, 14th mag Univ. of Hawaii: 19 dof, 12th mag San Pedro Martir (Baja CA): 19 dof Subaru: 19 dof Hokupaa on Gemini Telescope: 36 dof, 13-17th mag Hokupaa 85 (under construction): 85 dof Shack-Hartmann systems: tend to have more degrees of freedom but in general need brighter guide stars Lick: 61 dof, 13.5 mag Palomar: 241 dof Keck: 250 dof, 13.5 mag ADONIS: 50 dof (?), 13 mag VLT (ESO) NAOS 15feb03 Nelson wavefront sensing 29
Shearing Interferometer Split pupil into two and displace one wrt other and subtract 15feb03 Nelson wavefront sensing 30
Pyramid Sensing Combines ideas of knife edge test and S-H Focus star at vertex Light goes into 4 faces Lens images pupil (4) onto detector detector A slope error on pupil will cause light to go to one of 4 images For a given pupil region, 4 intensities gives slope 15feb03 Nelson wavefront sensing 31
Point Diffraction WFS 15feb03 Nelson wavefront sensing 32
Detectors for wavefront sensing Shack-Hartmann: usually use CCDs (charge-coupled devices), sizes up to 128 x 128 pixels Sensitive to visible light (out to ~ 1 micron) Can have high quantum efficiency (up to 85%) Practical frame rates limited to a few khz Read noise currently > 3 electrons per pixel per read New development: infrared detectors (more noise) Curvature: usually use avalanche photodiodes (1 pixel) Sensitive to visible light Slightly lower quantum efficiency than CCDs NO NOISE Very fast 15feb03 Nelson wavefront sensing 33
Phase Diversity Idea is to take two simultaneous images near the focus, with a known aberration between them (typically focus). The two (diffraction limited sampling) image intensities provide enough information to determine the wavefront error. Very non linear relationship- takes lots of computer time Image near focus Image in focal plane 15feb03 Nelson wavefront sensing 34
Summary of main points Wavefront sensors in common use for astronomy measure intensity variations, deduce phase Shack-Hartmann Curvature sensors Curvature systems are cheaper, have fewer degrees of freedom, scale more poorly to high no. of degrees of freedom, but can use fainter guide stars Shack-Hartmann systems excel at very large no. of degrees of freedom Complementary advantages Other methods under consideration 15feb03 Nelson wavefront sensing 35
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