Apochromatic lens design in the short-wave infrared band using the Buchdahl dispersion model

Wei Wang; Xing Zhong; Jiang Liu; Xiaoheng Wang

doi:10.1364/AO.58.000892

Applied Optics
Vol. 58,
Issue 4,
pp. 892-903
(2019)
•https://doi.org/10.1364/AO.58.000892

Apochromatic lens design in the short-wave infrared band using the Buchdahl dispersion model

Wei Wang, Xing Zhong, Jiang Liu, and Xiaoheng Wang

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Wei Wang, Xing Zhong, Jiang Liu, and Xiaoheng Wang, "Apochromatic lens design in the short-wave infrared band using the Buchdahl dispersion model," Appl. Opt. 58, 892-903 (2019)

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Abstract

Chromatic aberration is an important artifact that influences image quality. Thus, it should be optimized during lens design. However, the typical combination and selection method of glass materials for the visible band can hardly satisfy the apochromatic requirements of short-wave infrared (SWIR) lenses. Therefore, we propose a method of glass selection for apochromatic lens design in the SWIR band through vector operation based on the Buchdahl model and third-order aberration theory. The proposed method overcomes limitations of traditional methods and unstable calculation results of special material properties. A design example is presented, which indicates that the proposed method can correct the secondary spectrum in the SWIR band and simplify the design using ordinary mass-produced glasses.

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Catalog	Range of $α$	Optimum $α$	Max. Error	Glass
Schott	0.0071–0.8058	0.325	$6.2954 \times 10^{- 5}$	N-KZFS2
CDGM	0.0253–0.7636	0.412	$2.0915 \times 10^{- 5}$	ZF52
Corning	0.0456–0.6535	0.411	$1.4386 \times 10^{- 5}$	E0525
SUMITA	0.0432–0.8049	0.462	$3.6699 \times 10^{- 5}$	KPSFN173
Pilkington	0.0145–0.9054	0.433	$1.0729 \times 10^{- 4}$	JLAK8

Material	$N_{0}$	$ν_{1}$	$ν_{2}$	$ν_{3}$	Max. Error
${CaF}_{2}$	1.42722	−0.004915	−0.000888	−0.002316	$3.021204 \times 10^{- 6}$
Silica	1.44714	−0.010405	−0.006511	−0.007111	$5.397995 \times 10^{- 6}$
H-FK61	1.48785	−0.007077	−0.001479	−0.003239	$3.103174 \times 10^{- 6}$
ZF12	1.72755	−0.021045	−0.002266	−0.012215	$8.360192 \times 10^{- 6}$
BK7	1.50372	−0.012059	−0.012059	−0.005197	$3.307846 \times 10^{- 5}$
N-SF66	1.87225	−0.027296	0.0030493	−0.014697	$2.113214 \times 10^{- 5}$

Glass Combination	$α_{1}$	$α_{2}$	$α_{3}$	Length
H-FK61/H-K3/ZF52	2.4302	−1.0651	−0.3650	$7.7159 \times 10^{- 5}$
H-FK61/H-F51/TF3	2.2424	−0.0992	−1.1432	$9.0584 \times 10^{- 5}$
H-FK61/H-K9L/ZF52	2.5610	−1.2000	−0.3636	$3.2415 \times 10^{- 4}$
H-FK61/H-F51/H-ZBaF1	2.7000	−0.3191	−1.3806	$1.3640 \times 10^{- 4}$
H-FK61/H-F51/H-ZK5	2.6977	−0.4493	−1.2485	$8.6891 \times 10^{- 4}$

Glass Combination	$α_{1}$	$α_{2}$	Length
H-FK61/H-K12	3.0703	−2.0703	0.0014
H-FK61/TF3	2.3393	−1.3393	0.0015
H-FK61/H-F4	2.0265	−1.0265	0.0026
H-FK61/H-ZF3	1.7586	−0.7586	0.0034
H-FK61/ZF12	1.8282	−0.8282	0.0050

Items	Requirements
Focal length	137.5 mm
Operating wavelength	1.0–1.7 μm
Relative aperture	1:4
Detector	$640 \times 512 pixels$
Pixel size	$25 \times 25 μm$

Lens	Front Surface	Back Surface
$r_{1} > 0$ $r_{2} < 0$	$Reduce ↓$	$Reduce ↓$
$r_{1} < 0$ $r_{2} > 0$	$Rise ↑$	$Rise ↑$
$r_{1} > 0$ $r_{2} > 0$	$Rise ↑$	$Reduce ↓$
$r_{1} < 0$ $r_{2} < 0$	$Reduce ↓$	$Rise ↑$

Items	Value
$Surface irregular / λ$	0.2–0.5
Radius/mm	0.1–0.15
Thickness/mm	0.01–0.02
Decenter/mm	0.01–0.02
Tilt	30”–50”
Refractive index	$3 \times 10^{- 4} â€“ 5 \times 10^{- 4}$
Abbe number	0.5%–1.0%

Glass	ZF52	H-FK61	H-K9L	H-FK61	H-ZF3
$n_{0}$	1.8059	1.4878	1.5038	1.4878	1.6863
$ϕ_{0}$ (norm)	−0.3636	2.5610	−1.2000	1.8285	−0.8285
$r_{1}$	46.52	37.86	−32.41	−49.89	47.96
$r_{2}$	37.86	−32.41	−206.96	47.96	130.20

Glass	ZF52	H-FK61	H-K9L	H-FK61	H-ZF3
$n_{0}$	1.8059	1.4878	1.5038	1.4878	1.6863
$ϕ_{0}$	−0.003967	0.027938	−0.013091	−0.016623	0.007532
$r_{1}^{'} / mm$	48.71	33.46	−32.41	−49.89	48.63
$r_{2}^{'} / mm$	37.86	−32.41	−215.4909	49.22	130.20
$d_{center} / mm$	4	11.5	4	4	4.5
$d_{rim} / mm$	4.5	3.2	7.8	7.4	3.4

Glass	ZF52	H-FK61	H-K9L	H-FK61	H-ZF3
$n_{0}$	1.8059	1.4878	1.5038	1.4878	1.6863
$ϕ_{0}$ (norm)	−0.3636	2.5610	−1.2000	1.8285	−0.8285
$r_{1}$	46.52	37.86	−32.41	−49.89	47.96
$r_{2}$	37.86	−32.41	−206.96	47.96	130.20

Glass	ZF52	H-FK61	H-K9L	H-FK61	H-ZF3
$n_{0}$	1.8059	1.4878	1.5038	1.4878	1.6863
$ϕ_{0}$	−0.003967	0.027938	−0.013091	−0.016623	0.007532
$r_{1}^{'} / mm$	48.71	33.46	−32.41	−49.89	48.63
$r_{2}^{'} / mm$	37.86	−32.41	−215.4909	49.22	130.20
$d_{center} / mm$	4	11.5	4	4	4.5
$d_{rim} / mm$	4.5	3.2	7.8	7.4	3.4

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