Paraxial Differential Transfer Coefficients of a Lens System*

Marc G. Dreyfus

doi:10.1364/JOSA.38.000703

Journal of the Optical Society of America
Vol. 38,
Issue 8,
pp. 703-705
(1948)
•https://doi.org/10.1364/JOSA.38.000703

Paraxial Differential Transfer Coefficients of a Lens System

Marc G. Dreyfus

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Marc G. Dreyfus, "Paraxial Differential Transfer Coefficients of a Lens System*," J. Opt. Soc. Am. 38, 703-705 (1948)

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Abstract

A shorter method is given for computing C(u_i′) and C(y_i) for paraxial rays than that described by F. D. Cruickshank (see reference 1), and a calculation plan is given for computing the rate of change of position of an axial ray in the image space per change in curvatures, indices of refraction, and separations of lens elements.

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Regular plan for ith surface		Special formulas
(1)=l_i′(2⁻)		(1_k)=l_k′
(2)=(1)/l_i	$= \underset{u_{i} \to 0}{Lim} (u_{i} / {u_{k}}^{'}) Cf$ .*
(3)=n_i	=N_i/N_i′
(4)=l_i−r_i
(5)=[(3)−1](1)²N_i′	=−[1−n_i]l_i′²(u_i₊₁/u_k′)²N_i′
	=−[1−n_i]l_i′(u_i₊₁)/(u_k′²)l_iu_iN_i′=∂l_k′/∂c_i
(6)=(2)²N_i	=(u_i/u_k′)²N_i=∂l_k′/∂_id_i₋₁
(7)=(1)(2)(4)/r_i	=(u_i/u_k′)²l_i[(l_i−r_i)/r_i]	(7P)=−(1)(2)
(8)=(7⁻)−(3)(7)	=∂l_k′/∂N_i′	(8_k)=−(3)(7)

Surface→	8	7	6	5	4	3	2	1
l_i	57.518	45.811	−14.814	−217.34	−206.19	−8.5000	−4.5000	−2.0000
l_i′	35.949	65.018	52.311	−9.3143	−212.84	−202.69	−6.0000	−3.0000

Surface→	8	7	6	5	4	3	2	1
1	35.949	40.636	46.402	29.174	28.570	28.085	19.825	13.217
2	.62500	.88703	−3.1322	−.13423	−.13856	−3.3042	−4.4056	−6.6083
3	1.6000	1.0625	.58824	1.6000	.96875	.64516	1.5000	.66667
4		37.811	−21.814	−223.34		−13.500	−1.5000
5	775.38	165.13	−1507.2	510.69	−40.814	−433.84	196.52	−87.341
6	.62500	1.3376	9.8108	.02883	.02976	10.918	29.114	43.670
7	−22.468	170.37	452.93	145.77	3.9588	250.56	−43.670	87.341
8	35.949	−203.48	96.063	219.69	141.94	−157.69	316.06	−101.90

Regular plan for ith surface		Special formulas
(1)=l_i′(2⁻)		(1_k)=l_k′
(2)=(1)/l_i	$= \underset{u_{i} \to 0}{Lim} (u_{i} / {u_{k}}^{'}) Cf$ .*
(3)=n_i	=N_i/N_i′
(4)=l_i−r_i
(5)=[(3)−1](1)²N_i′	=−[1−n_i]l_i′²(u_i₊₁/u_k′)²N_i′
	=−[1−n_i]l_i′(u_i₊₁)/(u_k′²)l_iu_iN_i′=∂l_k′/∂c_i
(6)=(2)²N_i	=(u_i/u_k′)²N_i=∂l_k′/∂_id_i₋₁
(7)=(1)(2)(4)/r_i	=(u_i/u_k′)²l_i[(l_i−r_i)/r_i]	(7P)=−(1)(2)
(8)=(7⁻)−(3)(7)	=∂l_k′/∂N_i′	(8_k)=−(3)(7)

Surface→	8	7	6	5	4	3	2	1
l_i	57.518	45.811	−14.814	−217.34	−206.19	−8.5000	−4.5000	−2.0000
l_i′	35.949	65.018	52.311	−9.3143	−212.84	−202.69	−6.0000	−3.0000

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Equations (10)

Journal of the Optical Society of America