Calculation of a diffraction corrector to control free-form surfaces

Authors: Krasnov D.I.
Published in issue: #8(73)/2022
DOI: 10.18698/2541-8009-2022-8-819
Category: Instrument Engineering, Metrology, Information-Measuring Instruments and Systems | Chapter: Laser and opto-electronic systems
Keywords: interference control, autocollimation branch, diffraction element, wavefront corrector, phase profile, free-form surface, interferometer, numerical methods
Published: 07.10.2022

A review of the autocollimation measuring branch of the interferometer to control free-form surfaces using a diffracted optical element as a wavefront corrector is presented. An algorithm for calculating the phase profile of a diffractive optical element and an algorithm for determining the coordinates of its zones required for fabrication are developed and adapted. As an example, the calculation of a diffractive element to control a free-form mirror, the deformation of which is described by the sum of Zernike polynomials, is carried out. The proposed method of control allows the certification of any concave surfaces, and with the use of auxiliary elements - any convex surfaces. For correct installation of the corrector in the working position, the auxiliary diffraction elements on the substrate periphery are provided.

References

[1] Challita Z., Agócs T., Hugot E. et al. Design and development of a freeform active mirror for an astronomy application. Opt. Eng., 2014, vol. 53, no. 3, art. 031311. DOI: https://doi.org/10.1117/1.OE.53.3.031311

[2] Xie Y., Mao X., Li J. et al. Optical design and fabrication of an all-aluminum unobscured two-mirror freeform imaging telescope. Appl. Opt., 2020, vol. 59, no. 3, pp. 833–840. DOI: https://doi.org/10.1364/ao.379324

[3] Muslimov E., Hugot E., Jahn W. et al. Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture. Opt. Express, 2017, vol. 25, no. 13, pp. 14598–14610. DOI: https://doi.org/10.1364/oe.25.014598

[4] Hu X., Hua H. High-resolution optical see-through multi-focal-plane head-mounted display using freeform optics. Opt. Express, 2014, vol. 22, no. 11, pp. 13896–13903. DOI: https://doi.org/10.1364/oe.22.013896

[5] Benítez P., Miñano J.C., Grabovickic D. et al. Freeform optics for virtual reality applications. Optical Design and Fabrication, 2017, paper ITu2A.1. DOI: https://doi.org/10.1364/IODC.2017.ITu2A.1

[6] Zhang H., Wang X., Xue D. et al. Modified surface testing method for large convex aspheric surfaces based on diffraction optics. Appl. Opt., 2017, vol. 56, no. 34, pp. 9398–9405. DOI: https://doi.org/10.1364/ao.56.009398

[7] Lukin A.V., Melnikov A.N., Skochilov A.F. Measurement of convergent mirror of millimetron telescope using computer-generated hologram. Fotonika [Photonics Russia], 2016, no. 5, pp. 44–48. DOI: https://doi.org/10.22184/1993-7296.2016.59.5.44.48 (in Russ.).

[8] Lukin A.V., Melnikov A.N., Skochilov A.F. Laser interferometer with aspherical holographic test glass for thermal vacuum chamber. Opticheskiy zhurnal, 2017, vol. 84, no. 3, pp. 65–66 (in Russ.). (Eng. version: J. Opt. Technol., 2017, vol. 84, no. 3, pp. 212–213. DOI: https://doi.org/10.1364/JOT.84.000212)

[9] Odinokov S.B., Sagatelyan G.R., Kovalev M.S. Raschet, konstruirovanie i izgotovlenie difraktsionnykh i gologrammnykh opticheskikh elementov [Calculation, design and production of diffraction and hologram optical elements]. Moscow, Bauman MSTU Publ., 2014 (in Russ.).

[10] Odinokov S.B., Sagatelyan G.R., Kovalev M.S. et al. Features of the plasma-chemical etching of quartz glass during the formation of deep surface relief on high-precision components of devices. Opticheskiy zhurnal, 2019, vol. 86, no. 5, pp. 70–77. DOI: https://doi.org/10.17586/1023-5086-2019-86-05-70-77 (in Russ.). (Eng. version: J. Opt. Technol., 2019, vol. 86, no. 5, pp. 317–322. DOI: https://doi.org/10.1364/JOT.86.000317)