INTERFEROMETRIC MEASUREMENTS
B. How to use ZYGO – GPI
Launch the MetroPro software under the ‘Eleve’ session and click on the “TP2A-Aberrations.app” application.
1.
Adjustments of the optical system under test
The optical set-up is easy and quick to align.
► In ‘Align Mode’ (ALIGN), make sure that the reference flat is well aligned: the retro-reflection should hit the target, on the video monitor.
► The optical system under test should be carefully centered on the pupil of the ZYGO and on the axis of the ZYGO. Align it by auto-collimation, i.e. by using a small aluminized flat mirror and by looking at the retro-reflection on the video monitor.
► Choose a spherical mirror that is well adapted to the back focal length of the lens under test.
► Adjust the position of the optical system under test so that it focuses the incoming laser beam onto the center of curvature of the spherical mirror (not on the vertex of the mirror!). This is done by auto-collimation again.
► In ‘View Mode’ (VIEW), adjust finely the position of the mirror to obtain a flat interferogram, or to minimize the number of fringes.
► Adjust the FOCUS in order to conjugate the pupil of the system under test with the measurement plane.
► Adjust the ZOOM in order to obtain a large image of the pupil on the video monitor, without clipping.
2. Adjustments of the optical system under test
► Enter the f-number of the lens under test (f-number).
► Launch the wavefront measurement by clicking on MESURE. The software uses a phase-shifting method: it reconstructs the wavefront from the acquisition of 7 interferograms, for 7 positions of the flat reference.
► By default, the software defines a circular mask that covers 98% of the pupil (Masque Auto: Yes). You can visualize the mask in the ‘Masque” window (clicking on MASQUES) or on the video screen. You can also define it yourself by un-clicking on Masque Auto: Yes, and then select ‘Acq’ (acquisition mask) and define your mask (“Define’).
► The Topographie du front d’onde window displays the wavefront and the statistics of the wavefront (PV and RMS values). Some defects may be subtracted from the measured wavefront before display, such as the Piston (PST), the Tilt (TLT), the sphere that best fits the wavefront (PWR), and 3rd order aberrations such as spherical aberration (SA3), coma (CMA) and
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astigmatism (AST). The substraction of one of these terms may be observed without launching another wavefront measurement by clicking ANALYSE.
► The Profil du Front d’Onde window allows you to plot a profile of the wavefront along any cross-section.
► The Décomposition Modale window displays the first 36 Zernike polynomial coefficients and the Seidel coefficients for 3rd order aberrations, in units of λ. The quality of the fit is also displayed (rms): it corresponds to the RMS value of the residuals. See Table 1 in the “GENERAL PRESENTATION OF THE ABERRATIONS LAB SESSIONS”.
The Seidel coefficients are calculated from the 3rd order Zernike coefficients. They are displayed together with the TILT and FOCUS, which are calculated with respect to the paraxial focus. These coefficients correspond to the OPD on the edge of the pupil, in units of λ, and are calculated by using the following relationships:
Institut d’Optique Graduate School Labwork sessions
It is noteworthy that these relationships are valid if the lens exhibits 3rd – order aberrations only; it is thus absolutely necessary to check whether high-order aberrations are negligible before using them.
2.
Diffraction analysis
The ZYGO software can simulate the PSF and the MTF from the measured wavefront, by Fourier Transform.
► You need to enter the ‘F-number’ in order to obtain relevant values for the PSF and the MTF.
► The Réponse Percussionnelle window calculates the PSF of the optical system and displays the Strehl ratio, i.e. the maximum intensity normalized to the maximum intensity reached by a diffraction limited system. It takes into account the subtracted defects (PST, TLT, PWR…).
Encircled Energy displays the integrated power versus the radial coordinate.
Cursors (right click >> Show Controller) give access to values of the encircled energy plot. You may change the resolution of the calculation of the PSF by changing the point size (‘taille du point’). For instance, HiRes will let you evaluate the size of the PSF with a better accuracy for systems with little aberration.
1 The Seidel polynomial associated to ASTIGMATISM is of the form u2cos2φ, which differs slightly from the standard form introduced in the Optical Design course at IOGS u2cos2φ). The u2cos2φ form follows the Born &
Wolf definition. The astigmatism coefficient calculated by ZyMOD/PC thus corresponds to the Peak-to-Valley amplitude of the OPD associated to astigmatism, and not to the amplitude of the OPD on the edge of the pupil (as is true for the other Seidel coefficients).
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► The Calcul de la FTM window displays the MTF, calculated by Fourier Transform of the PSF, along 4 directions. The cut-off frequency 1/λN is calculated from the f-number. The MTF profiles are displayed with the following color code: 0° (dark blue lozenges), 90° (green triangles), +45° (light blue squares), and -45° (red).
Institut d’Optique Graduate School Labwork sessions 40
C.
Preliminary calculations
The specifications of the lenses are gathered p.11.
1.
Doublet in the best orientation
Q1- What is the doublet f-number? What is its image numerical aperture?
Q2- What is the diameter of the image spot if the doublet is diffraction limited?
Q3- What is the value of the doublet MTF cut-off frequency at 0% assuming that it is diffraction limited?
2.
Magnifying objective
The magnifying objective will be studied at N=5.6 on axis and at the edge of the field of view (y’= 22 mm).
Q4- What would be the diameter of the image spot if the objective was diffraction limited?
Q5- What is the cut-off frequency of the MTF of the objective assuming it is diffraction limited ? and for 10% and 50% MTF values ? How these values are modified for increasing N values ?
Q6- What is the maximal useful field angle of this objective?
B.
Measurements
1.
Doublet in the best orientation i) Wavefront measurement
ON AXIS► Place the doublet in the best orientation on axis and adjust it in order to obtain a flat interferogram.Enter the f-number into the software.
? What is the variation of the wavefront error between two consecutive fringes?
► Evaluate the maximum OPD by observing the interferogram on the video monitor. Then, launch the wavefront measurement by the ZYGO. Make sure that the measurement is performed at the best focus.
? How do you make sure that the measurement is performed at the best focus?
? Why should you subtract the tilt and power terms (TLT and PWR)?
? What is the value of the maximum OPD measured by the ZYGO (PV and RMS)? Does it fulfill the Maréchal criterion?
? What are the main aberration terms here? What is their order? Compare to the simulation (cf. Appendix 2).
? How can you evaluate the precision of your measure?
Call the professor to cross-check your observations.
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► Calculate the PSF. Analyze the shape and the dimension of the PSF. Plot the encircled energy and compare your result with the encircled energy diagram of an Airy function.
? What is the Strehl ratio of the PSF. Is the doublet diffraction limited on axis?
? Is this result consistent with the measurement of the PSF performed by the point source method (see LAB SESSION N°1)?
► Calculate the MTF and compare your result with the MTF of a diffraction limited system in the same conditions.
? What is the spatial frequency that corresponds to a visibility of 10% and 50%
for a sinusoidal target?
ii) Wavefront measurement OFF AXIS
► Turn the objective around the vertical axis to clearly observe astigmatism (field angle θ=5°). Measure precisely the rotation angle. Observe the different interferograms when the center of curvature of the spherical mirror is respectively at the sagittal focus, the best focus and the tangential focus. Perform the following characterization for each position:
► Measure the wavefront and explain the shape of your result.
? Deduce from your 3 measurements the amplitude of the astigmatism and the associated uncertainty.
► Calculate the PSF.
? Is the doublet diffraction limited in this configuration? Compare the PSF to the Airy function and to the PSF that you obtained on axis.
? Calculate the PSF. What is the Strehl ratio? What is the radius of a disk that encircles 84% of the energy?
? Compare your result to the direct measurements of the PSF that you performed by the point source method (see LAB SESSION N°2).
► Launch the MFT calculation. Determine the spatial frequency at 50 and 10%
visibility. Compare your results to the results that you obtained on axis and to the MTF of a perfect system. In particular, observe how the shape and the symmetries of the MTF are related to the shape and symmetries of the PSF.
► Call the professor to cross-check your observations.
2.
Doublet in the worst orientation
► Place the doublet in the worst orientation and adjust it so that it operates on axis: the interferogram should have the symmetry of revolution.
► Observe the evolution of the interferogram for different positions of the center of curvature of the spherical mirror: paraxial focus, best focus, and marginal focus.
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? How do you recognize which focus is which?
Call the professor to cross-check your observations.
i) Observation at the best focus
► Place the center of curvature of the spherical mirror at the best focus and answer the same questions as previously.
► Evaluate the amplitude of the OPD on the edge of the pupil by observing the interferogram on the video monitor. Then, launch the wavefront measurement.
? Evaluate the PV and RMS OPD measured by the ZYGO?
Compare with your observation on the video monitor. Is the doublet diffraction limited in this configuration?
► Analyze the wavefront decomposition on the Zernike basis and on the Seidel basis. Verify by yourselves the calculations of the Seidel coefficients done by the ZYGO.
? What is the main aberration of the doublet in this configuration?
► Calculate the PSF. Evaluate the Strehl ratio in this configuration and the radius of the disc that encircles 84% of the energy.
? Compare the calculation of the PSF performed by the ZYGO at the best focus to the direct observation performed in LAB SESSION N°1 by the point source method.
? Compare to the result obtained for the doublet in the best orientation.
► Calculate the MTF of the doublet. Compare the result to the MTF of a diffraction limited lens, et determine the cut-off frequency at 10%.
? Are the shape and the symmetry of the MTF related to the shape and the symmetry of the PSF?
ii) Observation in the paraxial focus
► Place the center of curvature of the spherical mirror on the paraxial focus of the doublet by translating the mirror longitudinally.
? What is the shape of the interferogram at the paraxial focus?
► Evaluate the amplitude of the OPD on the edge of the pupil by observing the interferogram on the video monitor. Then, launch the wavefront measurement. Check that the spherical term (PWR) is not removed for this measurement.
? Why is it important to keep the spherical term here?
? Evaluate the PV and RMS OPD measured by the ZYGO? Compare with your observation on the video monitor. Is the result compatible with the measurement done at the best focus?
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? Is the name “best focus” relevant to describe the previous configuration? How is it defined?
► Analyze the wavefront decomposition on the Zernike basis and on the Seidel basis. By comparing the measurements done at the various foci, evaluate the uncertainty on the coefficients of the main aberrations.
► Simulate the PSF. Observe the shape and dimension of the PSF.
? Is this calculation valid?
3.
Study of a magnifying objective
► Enter the f-number of the objective into the software
► Study the aberrations of this objective on axis, at full aperture, and at the edge of the field of view (y’= 22 mm).
► Analyze the wavefront decomposition on the Zernike basis and the amplitude the OPD.
? What are the main aberrations of this lens?
? Does it fulfill the Maréchal criterion on axis? At full field?
? What are the uncertainties of these measures?
► Evaluate the dimension of the PSF on axis and at full field.
► Evaluate the MTF of this objective on axis and at the edge of the field of view.
What is the spatial frequency at 10% visibility?
? What do you think are the most relevant parameters to evaluate the performance of this lens?
? Compare your results to those obtained by the point source method (see LAB SESSIONS N°1 & 2).
? Comment on your results in the perspective of photography applications. What are your conclusions?
? What other measurements are absolutely necessary to fully characterize the performance of this objective, in the perspective of photography applications?
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