WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Wavefront sensing with varying transmission filters: Past, present and future François Hénault CRAL - Observatoire de Lyon, 9 Avenue Charles André, 69561 Saint-Genis-Laval, France
OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
• Basic principle: to observe the pupil through a transmissive filter at the image plane Optical Y System under testing Input Wavefront
Exit Pupil Tested Wavefront
Pupil Imaging Lens
Observing Plane
Z Varying density filter
OPTICAL FABRICATION, TESTING, AND METROLOGY II
Image Plane
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
A few words of History (the past) Y
O
• Foucault Knife-edge test is the simpler and older filter (1859) Y X
Y’ O’
Exit Pupil
X
Image Plane
Foucault Knifeedge
X’
Pupil Observing System (CCD camera)
OPTICAL FABRICATION, TESTING, AND METROLOGY II
Pupil Image
Z Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
A few words of History (cont’d) • Movable Foucault knife-edges allow quantitative information on WFE slopes to be retrieved (Gaviola 1936) • Last WFE sensor developed for astronomy is based on previous idea (Pyramidal WFS, Ragazzoni 1993) • First varying transmission filter proposed by Sprague & Thompson (1972), then Horwitz (1978), but only used in phase contrast microscopy (i.e. filter located in Pupil plane rather than Image plane) • First real WFS based on this principle proposed by Bortz (1984) and simplified by Oti (2003). Sometimes called "optical differentiation WFS"
OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
• Encoding pupil intensities using a gradient-spatial filter: x M y Y Y O
X
Y’
M’
X
Image Plane
O’ Exit Pupil
x’ y’
Varying density filter
X’
Pupil Observing System (CCD camera)
OPTICAL FABRICATION, TESTING, AND METROLOGY II
Pupil Image
Z Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Various proposed filter shapes • Sprague & Thompson’s filter with different parameters x’1 < x’0 x’1 = x’0 x’1 > x’0
T( x’) 1 0.5
-x’0
-x’1
0
OPTICAL FABRICATION, TESTING, AND METROLOGY II
x’1
x’0
X’
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Various proposed filter shapes Amplitude TransmissionsAt(x') 1
0.75
0.5
Foucault Linear Amplitude Linear Intensity (Horwitz)
0.25
Sine Amplitude Sine Intensity
0 -0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
X' (mm)
OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
The present • General study to be published in: F. Hénault, “Wavefront sensor based on varying transmission filters: theory and expected performance,” Journal of Modern Optics, Vol. 52, n°14
• Geometric optics theory: simple relationship between measured intensities IX(x,y) and the WFE δ(x,y) x 1 ' I X ( x, y ) ∂δ (x, y) = − 1 ∂x D IN • Intuitive conclusions – The formula is wavelength-independent. Wide-spectrum lamps or luminous sources can be used – The highest filter slopes, the best measurement sensitivity and accuracy ? OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
• In Fourier optics theory, the expression of the filtered amplitude A(x,y) is not so simple: 1 2π x '0 x 2π 2x' 0 (when x’1 < x’0) B R (x, y) exp i δ(x, y) ⊗ sinc λD 2 λ λD 1 ∂δ(x, y) λ ∂B R (x, y) 2π x '1 x 2π 2 + B R (x, y) −i exp δ(x, y) ⊗ sinc i λ λ ∂x ∂x 2 2π λD π ( x '0 -x '1 ) x π ( x '0 + x '1 ) x 2π x ' -x ' + i B R (x, y) exp i δ(x, y) ⊗ 0 1 sinc × sin λD λD λ λD
A X ( x, y) =
WFE slopes
6
WFE difference
• Add oscillatory terms to retrieved slopes and WFE (intrinsic measurement error):
0
-6 -1.25
0
1.25
OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Development of an end-to-end numerical model Begin
Import pupil WFE from an external file
For two different orientations of the filter (along X and Y-axes):
Compute complex amplitude in pupil plane
Compute complex amplitude in image plane via Fourier transform
Multiply by the filter transmission function
End For
Compute filtered amplitude A(x,y) via inverse Fourier transform
Reconstruct WFE from its slopes using “classical” algorithms (e.g. Southwell)
Compute the measured intensity I(x,y) = | A(x,y) |2
Compare retrieved and initial WFEs and compute their difference maps
Deduce WFE slope using geometrical optics approximation
OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
End
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Main results and conclusions (so far) • Diffraction effects generate intrinsic measurement error, e.g. high spatial frequency oscillations • Measurement accuracy greatly enhanced when removing the pupil rim (over 1-2 pixel width) • The filter slope 1/x’1 must be matched to the measured WFE. Best results are obtained when x’1 ≈ x’0 • Then, intrinsic errors are well below λ/10 PTV and λ/100 RMS • Different filter shapes are possible (e.g. sine intensity transmission) • Very large geometrical aberrations can be evaluated • Extended spatial sources can be used within certain limits OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Measuring a parabolic mirror from its(C)curvature centre (A) WFE reference map (B) PSF in image plane (log. scale) Measured slope along X-axis
(D) Measured slope along Y-axis
(E) Reconstructed WFE
(F) WFE difference map
• Accuracy 0.5 % PTV and 0.06 % RMS OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Using extended luminous source 6.0
Square Source (PTV) Error Ratio (%)
5.0
Circular Source (PTV) Square Source (RMS)
4.0
Circular Source (RMS) 3.0 2.0 1.0
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0.0
Source Radius (mm)
• Source may be extended to 15-20 times the Airy disk radius OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
The future: manufacturing prototypes • Option 1: Simultaneous slope measurements Exit Pupil
X Image Plane
Measurement Head Beam-splitter
Tested Wavefront
CCD Camera 1
Z
Y
OPTICAL FABRICATION, TESTING, AND METROLOGY II
CCD Camera 2
Image Plane (symmetrical)
Y Varying density filters Y X
X
Wavefront slopes Jena, 15 September 2005
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Y • Option 2: Sequential slope measurements Exit Pupil
Measurement Head
Tested Wavefront
Varying density filters Rotation axis
Image Plane
CCD Camera
Z Motor
Y
X
Filter wheel
Y
Wavefront slopes OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
X
WFE sensing with varying transmission filters: Past, present and future
SPIE International Symposium on
Conclusion • WFS with varying transmission filters represent a good alternative to other existing techniques (interferometers, Shack-Hartmann..) provided that certain precautions are taken • Prototypes should be manufactured and tested to confirm their performance • The effects of some factors remain to be studied: – Non-uniformity of the incident beam – Noises and non-linearity of the CCD detector – Tolerances on the actual profile of the gradient density filter OPTICAL FABRICATION, TESTING, AND METROLOGY II
Jena, 15 September 2005
