Optical MTF and aberration predictions with the Helmholtz-Lagrange invariant

P. Sandri

doi:10.1364/AO.520107

Applied Optics
Vol. 63,
Issue 13,
pp. 3390-3398
(2024)
•https://doi.org/10.1364/AO.520107

Optical MTF and aberration predictions with the Helmholtz-Lagrange invariant

P. Sandri

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P. Sandri, "Optical MTF and aberration predictions with the Helmholtz-Lagrange invariant," Appl. Opt. 63, 3390-3398 (2024)

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Abstract

The paper presents a method for a rough estimation of the aberrations and of the MTF of an optical system by means of the Helmholtz-Lagrange invariant. The method allows for a rough understanding of an optical design and can find application in those cases where approximated performance predictions are needed, for example, before running complex and time-consuming analyses. The simple approach presented here is a rough approximation and should always be followed by the usual tolerance analyses.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the author upon reasonable request.

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Equations (14)

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Focal Length [mm]	1200
Entrance pupil diameter [mm]	200
Wavelength [µm]	1,064
Field of view across-track/along-track [°]	$\pm 2 / \pm 1, 5$
F/number	6
Image space NA	0,083
Cutoff freq. [l/mm]	156,6
HL invariant $I$ of the design [mm]	4,362
$Δ I$ in nominal design [mm]	0,0056
Total aberration $Δ l_{k}^{'}$ in design [mm]	0,067
${W F E}_{rms}$ in design [ $λ$ ]	0,015
Max spot diagram from Zemax [mm]	0,020
Max ${W F E}_{rms}$ from Zemax [ $λ$ ]	0,019

Description	Radius [mm]	Distance [mm]	Conic Constant	Material
Mirror M1	−2260,6365	−576,1893	−1,67104	Mirror
Mirror M2 - Stop ∅120 mm	−778,48202	576,1893	−0,48533	Mirror
M3	−1169,07098	−814,2007	$+$ 1,21245	Mirror
Window	Infinity	−3,6	0	Fused silica
	Infinity	−30,998	0	Air
Image plane

Focal length [mm]	330
Entrance pupil diameter [mm]	140
Wavelength [µm]	10
Field of view across-track/along-track [°]	$\pm 1, 65 / \pm 0, 19$
F/number	2,36
Image space NA	0,212
Cutoff freq. [l/mm]	42,42
HL invariant $I$ of the design [mm]	2,029
$Δ I$ in nominal design [mm]	0,016
Total aberration $Δ l_{k}^{'}$ in design [mm]	0,076
${W F E}_{rms}$ in design [ $λ$ ]	0,038
Max spot diagram from Zemax [mm]	0,090
Max ${W F E}_{rms}$ from Zemax [ $λ$ ]	0,049

Focal length [mm]	60
Entrance pupil diameter [mm]	20
Wavelength [µm]	0,587
Field of view [°]	±2
F/number	3
Image space NA	0,167
Cutoff freq. [l/mm]	567,9
HL invariant $I$ of the design [mm]	0,349
$Δ I$ in nominal design [mm]	0,0009
Total aberration $Δ l_{k}^{'}$ in design [mm]	0,0054
${W F E}_{rms}$ in design [ $λ$ ]	0,015
Max spot diagram from Zemax [mm]	0,005
Max ${W F E}_{rms}$ from Zemax [ $λ$ ]	0,021

Description	Radius [mm]	Thickness [mm]	Material
Aperture Stop
Lens 1	66,44372	8,0	FK51
Lens 2	−39,7894	2,5	SSKN8
	−241,18174	0,5	Air
Lens 3	138,69134	5,0	BK7
	519,3487	35,65	Air
Lens 4	67,24775	6,0	LAK8
Lens 5	−48,41635	2,8	SF6
	−186,03256	30,683	Air
Image plane	Infinity

Abstract

Data availability

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Tables (5)

Equations (14)

Applied Optics