Canonical properties of optical-design modules

O. N. Stavroudis; R. I. Mercado

doi:10.1364/JOSA.65.000509

Journal of the Optical Society of America
Vol. 65,
Issue 5,
pp. 509-517
(1975)
•https://doi.org/10.1364/JOSA.65.000509

Canonical properties of optical-design modules

O. N. Stavroudis and R. I. Mercado

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O. N. Stavroudis and R. I. Mercado, "Canonical properties of optical-design modules," J. Opt. Soc. Am. 65, 509-517 (1975)

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Abstract

Modules are conceived as building blocks in formulating optical designs with certain useful properties. This paper provides necessary and sufficient conditions for successfully combining (coupling) modules to form such a design system. Canonical ray tracing is defined, and canonical versions of aberration coefficients are derived. These are used to obtain equations for zero values of third-order-monochromatic and primary-chromatic-aberration coefficients. Their utilization in practical problems in optical design is illustrated.

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Module 1 (N₀ = 1.67003, N₁ = 1.4645, N₂ = 1.0)			Module 2 (N₀ = 1.67003, N₁ = 1.0, N₂ = 1.4645)			Module 3 (N₀ = 1.0, N₁ = 1.9525, N₂ = 1.4645)
Shape parameter	Critical value type^a	Category	Shape parameter	Critical value type^a	Category	Shape parameter	Critical value type^a	Category
Real Case			Real Case			Real Case
−1.000000	Minus one	D2	−1.000000	Minus one	D2	−1.000000	Minus one	C1
−0.300252	Psi/0	D2	−0.420983	Psi/0	D2	−0.149066	Psi/0	C1
−0.116419	Psi/br/prime	D1	−0.189096	Psi/inf	A2	0.000000	Psi/zero	D2
−0.108638	Psi/	A2	−0.161398	Psi/	D1	0.100839	Psi/	A1
−0.044795	Psi/inf	D2	−0.132476	Psi/br/prime	D2	0.137521	Psi/br/prime	A2
0.000000	Psi/zero	C1	0.000000	Psi/zero	C1	0.202123	Psi/inf	D2
1.000000	Plus one		1.000000	Plus one		1.000000	Plus one
Imaginary ease			Imaginary case			Imaginary case
0.000000	Phi/zero	D2	0.000000	Phi/zero	D2·	0.000000	Phi/zero	C1
60.000000	Pi/3	D2	60.000000	Pi/3	D2	60.000000	Pi/3	C1
180.000000	Pi/		180.000000	Pi/		180.000000	Pi/

Module 1 (D2)
Real case ψ = −0.109
T₀ = 1.686852,	C₁ = 2.070679	T₁ = −0.010242,	C₂ = −3.082274
E = 1.596664,		A = −0.048939
Y₀ = 0.000000	Ӯ₀ = 1.000000	spherical	= 0.000000
U₀ = −0.598792	Ū₀ = 0.626306	coma	= 1.747179
Y₁ = 1.010013	Ӯ₁ = −0.056423	astigmatism	= 0.000000
U₁ = −0.977615	Ū₁ = 0.730670	Petzval	= −0.802848
I₁ = 2.699295	Ī₁ = −0.743647	curvature	= 0.401424
Y₂ = 1.000000	Ӯ₂ = −0.048939	distortion	= 0.291347
U₂ = −0.000000	Ū₂ = 1.000000	axial color	= 0.001950
I₂ = −2.104660	Ī₂ = −0.579827	lateral color	= −0.008728
Module 2 (A2)
Real case ψ = −0.162
T₀ = 1.688639,	C₁ = −6.091306,	T₁ = 0.003564,	C₂ = −6.731617
E = 1.530472		A = −0.154843
Y₀ = 0.000000	Ӯ₀ = 1.000000	spherical	= 0.000006
U₀ = −0.598792	Ū₀ = 0.653393	coma	= 1.305327
Y₁ = 1.011143	Ӯ₁ = −0.103346	astigmatism	= 0.000000
U₁ = 3.126836	Ū₁ = 0.669396	Petzval	= −0.308795
I₁ = −5.560590	Ī₁ = −0.023884	curvature	= 0.154397
Y₂ = 1.000000	Ӯ₂ = −0.105731	distortion	= 0.009858
U₂ = 0.000000	Ū₂ = 0.682827	axial color	= −0.032416
I₂ = −9.858454	Ī₂ = 0.042345	lateral color	= −0.00548
Module 3 (A1)
Real case ψ = −0.102
T₀ = 1.035006,	C₁ = 3.575068,	T₁ = 0.027075,	C₂ = 5.173065
E = 1.264701		A = 0.237366
Y₀ = 0.000000	Ӯ₀ = 1.000000	spherical	= 0.000000
U₀ = −1.000000	Ū₀ = 0.790701	coma	= −1.143359
Y₁ = 1.035006	Ӯ₁ = 0.181720	astigmatism	= 0.000000
U₁ = 1.292935	Ū₁ = 0.721722	Petzval	= −0.861197
I₁ = 4.700216	Ī₁ = −0.141397	curvature	= 0.430598
Y₂ = 1.000000	Ӯ₂ = 0.162090	distortion	= −0.040547
U₂ = 0.000000	Ū₂ = 0.682827	axial color	= 0.028412
I₂ = 3.880130	Ī₂ = 0.116729	lateral color	= 0.007866

	Design 1: Zero Petzval sum	Design 2: Zero coma	Design 3: Zero axial color	Glass properties
	Design 1: Zero Petzval sum	Design 2: Zero coma	Design 3: Zero axial color	N	ΔN
F₁	−17.8715	−22.9655	−34.9089
F₂	18.8346	24.2031	36.7901
F₃	31.6167	31.6167	31.6167
t₀	0.854000	1.097420	1.668144	1.0	0.0
c₁	−0.172295	−0.134078	−0.088206
t₁	0.264020	0.339275	0.515718	1.4645	0.007063
c₂	0.115475	0.089861	0.059117
t₂	1.338239	1.719681	2.614017	1.67003	0.014222
c₃	−0.321918	−0.250514	−0.164805
t₃	0.031168	0.040052	0.060882	1.0	0.0
c₄	−0.352426	−0.274254	−0.189423
t₄	4.688810	3.851779	1.889265	1.4645	0.007063
c₅	−0.162851	−0.162851	−0.162851
t₅	0.684320	0.684320	0.684320	1.9525	0.046774
c₆	−0.113480	−0.113480	−0.113480
t₆	32.4973	32.4973	32.4973	1.0	0.0

	Design 1: Zero Petzval sum		Design 2: Zero coma		Design 3: Zero axial color
	Marginal	Principal	Marginal	Principal	Marginal	Principal
Pupil y	1.8750	0.36397	1.8750	0.	1.8750	0.36397
u	0.	0.36397	0.	0.36397	0.	0.36397
Sphere y	1.8750	−0.31083	1.8750	−0.39943	1.8750	−0.60715
u	−0.10246	0.26551	−0.07974	0.26551	−0.05246	0.26551
i	−0.32305	−0.31042	−0.25140	−0.31042	−0.16539	−0.31042
Sphere y	1.9021	−0.38093	1.9021	−0.48951	1.9021	−0.74409
u	−0.06282	0.22742	−0.04889	0.22742	−0.03216	0.22742
i	0.32210	−0.30950	0.25066	−0.30950	0.16490	−0.30950
Sphere y	1.9861	−0.68528	1.9861	−0.88061	1.9861	−1.3386
u	0.32348	0.23199	0.25173	0.23199	0.16561	0.23199
i	−0.57655	−0.00682	−0.44866	−0.00682	−0.29516	−0.00682
Sphere y	1.9760	−0.69251	1.9760	−0.88990	1.9760	−1.3527
u	0.	0.23582	0.	0.23582	0.	0.23582
i	−1.0199	0.01206	−0.79367	0.01206	−0.52213	0.01206
Sphere y	1.9760	−1.7982	1.9760	−1.7982	1.9760	−1.7982
u	−0.08043	0.25007	−0.08043	0.25007	−0.08043	0.25007
i	−0.32180	0.05702	−0.32180	0.05702	−0.32180	0.05702
Sphere y	2.0311	−1.9694	2.0311	−1.9694	2.0311	−1.9694
u	0.06250	0.27540	0.06250	0.27540	0.06250	0.27540
i	−0.15006	−0.02659	−0.15006	−0.02659	−0.15006	−0.02659
Image y	0.	−10.919	0.	−10.919	0.	−10.919
Spherical	0.		0.		0.
Astigmatism	0.		0.		0.
Coma	−0.0030574		0.		0.002663
Petzval sum	0.		−0.006114		−0.013454
Curvature	0.		0.002086		0.004591
Distortion	−0.032748		−0.032748		−0.032748
Axial color	−0.003396		−0.001853		0.
Lateral color	0.		0.		0.

Module 1 (N₀ = 1.67003, N₁ = 1.4645, N₂ = 1.0)			Module 2 (N₀ = 1.67003, N₁ = 1.0, N₂ = 1.4645)			Module 3 (N₀ = 1.0, N₁ = 1.9525, N₂ = 1.4645)
Shape parameter	Critical value type^a	Category	Shape parameter	Critical value type^a	Category	Shape parameter	Critical value type^a	Category
Real Case			Real Case			Real Case
−1.000000	Minus one	D2	−1.000000	Minus one	D2	−1.000000	Minus one	C1
−0.300252	Psi/0	D2	−0.420983	Psi/0	D2	−0.149066	Psi/0	C1
−0.116419	Psi/br/prime	D1	−0.189096	Psi/inf	A2	0.000000	Psi/zero	D2
−0.108638	Psi/	A2	−0.161398	Psi/	D1	0.100839	Psi/	A1
−0.044795	Psi/inf	D2	−0.132476	Psi/br/prime	D2	0.137521	Psi/br/prime	A2
0.000000	Psi/zero	C1	0.000000	Psi/zero	C1	0.202123	Psi/inf	D2
1.000000	Plus one		1.000000	Plus one		1.000000	Plus one
Imaginary ease			Imaginary case			Imaginary case
0.000000	Phi/zero	D2	0.000000	Phi/zero	D2·	0.000000	Phi/zero	C1
60.000000	Pi/3	D2	60.000000	Pi/3	D2	60.000000	Pi/3	C1
180.000000	Pi/		180.000000	Pi/		180.000000	Pi/

Abstract

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Figures (3)

Tables (4)

Equations (62)

Journal of the Optical Society of America