SHACK-HARTMANN WAVEFRONT ANALYSIS
C. Preparation questions
The following questions need to be answered before the lab sessions.
1. Principle and analysis of the HASO instrument
a. What are the shape and the size of the PSF of a micro-lens? Compare to the size of the pixels. Do you believe that the spatial sampling of the diffraction spot by the pixels is well suited to the calculation of the position of the barycenter?
b. The HASO cannot measure a wavefront with a radius of curvature smaller than 25 mm. What is the corresponding maximal numerical aperture which can be measured?
c. According to the manufacturer, the maximum measurable wavefront slope is 3°: what is the corresponding spot displacement with respect to the micro-lenses axis? Compare this value to a microlens size and comment.
2. Operating conditions of the doublet
The doublet should work for a conjugation ensuring a -1/3 magnifying ratio, and will be evaluated for a field angle between 0° and 2°. In the following we shall assume that it behaves as a thin lens.
a. What should be the distance between the point source and the lens under test in order to ensure the wanted magnifying ratio?
b. Estimate the numerical apertures (in object and image spaces), and compare them with the NA of the source fiber and the maximum NA measured by the HASO respectively.
c. Calculate the Airy spot diameter in the image plane. Compare the image of the fiber core diameter to this value.
d. What is the lateral position of the image corresponding to the 2° field angle?
3. Strehl ratio
a. Give the definition of the Strehl ratio.
b. Recall the Maréchal criterion, as defined on the root-mean square of the wavefront defect; at which value for the Strehl ratio does it correspond?
c. Recall the approximation of the root-mean square of the wavefront defect with the Zernike decomposition coefficients.
D.
Measurements
You will study the shape and the dimension of the PSF by the point source method after the magnifying objective and use the HASO to directly measure the wavefront. You will also compare your direct observation of the PSF with the one simulated by the HASO software.
1.
Direct analysis of the PSF on axis
► Switch on the laser diode (POWER, then ENBL ON) and adjust the current with the knob.
► Place the doublet lens in its best orientation and on axis; adjust its position with respect to the light source to ensure a transverse magnification gy = -1/3. Make sure that the beam fully illuminates the objective.
► Look at the PSF on the camera with the microscope viewer; be careful and avoid saturation of the CMOS sensor. Choose a microscope objective that ensures a sufficient resolution in the image. Adjust the lens orientation to make the PSF rotationally symmetric (this adjustment will be improved with the HASO later).
► Measure the size of the PSF on axis by using the microscope viewer in the best focus plane.
? Does it seem to you that this lens “diffraction limited” on axis at full aperture?
2.
Study of the lens on axis at full aperture with the HASO
► Follow the HASO adjustment procedure above (see A.5). Make sure that the stray light is minimized.
► Observe the image spots on the HASO CCD and compare their dimensions to the PSF of individual micro-lenses (see C.1.a).
? Evaluate roughly the number of micro-lenses that are illuminated and used for the wavefront measurement. This number is also given in the Slope window.
► Try to orient the lens on axis by observing and minimizing the Zernike coefficients associated to off-axis aberrations and minimizing the RMS amplitude of the wavefront defect σΔ.
► What is the numerical aperture measured by the HASO in these conditions?
Compare to your theoretical estimation in C.2.b, and deduce an experimental evaluation of the actual magnifying ratio of the setup.
Call the professor to cross-check your adjustments.
► Observe the measured wavefront. What is the defect amplitude, PV and RMS?
What are the main Zernike coefficients in the wavefront decomposition?
Institut d’Optique Graduate School Restricted diffusion Lab work sessions – Master Erasmus Mundus OpSciTech
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? Explain what FOCUS corresponds to and why FOCUS and TILT are not relevant to characterize the quality of the optical system under test.
IN THE FOLLOWING, ALWAYS SUBTRACT TILT AND FOCUS TO MEASURE THE WAVEFRONT DEFECTS.
► Evaluate the optical path delay (PV and RMS) of the wavefront with respect to the reference sphere.
? How does the RMS OPD compare to the Maréchal criterion?
? What are the main aberrations of the lens on axis, i.e. the aberrations that have amplitudes larger than the noise of the wavefront decomposition? For each of the aberrations evaluate the Peak-to-Valley amplitude in the Seidel basis.
► Evaluate the experimental accuracy of your wavefront measurements, i.e. the amplitude of the wavefront defects and the Zernike coefficients, by moving the HASO around whilst remaining in acceptable operating conditions. The history knob ( ) of the ΔRMS et ΔPV values can be helpful to evaluate your experimental accuracy.
► Simulate the PSF of the objective on axis with the HASO software. Evaluate the size of the PSF by using the cross sections.
? In which plane is the PSF calculated? Explain.
? What is the Strehl ratio value? Comments.
? Compare this numerical simulation of the PSF to your direct measurement with the camera.
3.
Fine study of the PSF through direct measurement
The doublet adjustements being now using the HASO measurements, resume the direct analysis of the PSF as observed with the microscope viewer on the camera.
► Save an image of the PSF and evaluate the diameter encircling 84% of light energy with the MatLab script.
► Observe how the PSF changes when you defocus forth and back from the best focus plane. What can you conclude regarding the performance of this lens?
► Observe the evolution of the PSF and of its maximum irradiance while decreasing the lens diaphragm diameter.
4.
Study of the doublet off axis at full aperture
► Turn progressively the lens around the vertical axis and measure both the wavefront (HASO) and the PSF (microscope viewer) for 0.5°, 1° and 2°. Take special attention to the evolution of:
• the different Zernike coefficients related to geometrical aberrations;
• the PV and RMS values of the wavefront defect;
• the shape and dimension of the PSF.
? Compare the simulations of the PSF deduced from the wavefront measurement to its direct measurement?
? Is the evolution of the Zernike coefficients with the field angle consistent with the 3rd order theory?
► At a field angle of 2°, find for which diaphragm diameters – and thus which NA – the PSF is diffraction-limited, both based on the wavefront measurement and on the direct observation of the PSF.
? Are these two measurements in agreement?
► At a field angle of 2°, find at which diaphragm diameters the PSF diameter is the smaller. Does it correspond to a maximum irradiance of the PSF?
► Summarize your analyses obtained from both methods for the doublet lens under these operating conditions.