Method of paraxial design of rifle scope with four-element image-erecting zoom system and high zoom factor

Antonín Mikš; Jiří Novák

doi:10.1364/AO.58.004787

Applied Optics
Vol. 58,
Issue 17,
pp. 4787-4796
(2019)
•https://doi.org/10.1364/AO.58.004787

Method of paraxial design of rifle scope with four-element image-erecting zoom system and high zoom factor

Antonín Mikš and Jiří Novák

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Antonín Mikš and Jiří Novák, "Method of paraxial design of rifle scope with four-element image-erecting zoom system and high zoom factor," Appl. Opt. 58, 4787-4796 (2019)

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Abstract

An analysis and a description of methods for a paraxial design of rifle scopes with a four-element image-erecting zoom system is performed. It is described a method of the calculation of basic design parameters of the rifle scope with the four-element image-erecting zoom system, where two inner elements are movable for ensuring zooming of the rifle scope. The method is demonstrated on two examples of the rifle scope design with the zoom factor $10 \times$ . Moreover, the possibility to design the rifle scope with the fixed position of the exit pupil using the four-element image-erecting zoom system with three movable elements is analyzed. The method of the initial paraxial design is demonstrated on two examples of the calculation of the basic rifle scope design parameters. The calculated parameters from proposed methods can be used in the aberration analysis and the optimization of the rifle scope parameters in optical design software.

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Equations (37)

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	$f_{2}^{'} = f_{3}^{'}$	$f_{2}^{'} = f_{3}^{'}$
$L_{23}$	$d_{\min} = 10$	$d_{\min} = 5$
60	15.6192	18.6898
70	19.3468	22.2604
80	22.9997	25.8247
90	26.6174	29.3853
100	30.2155	32.9434
110	33.8016	36.5000
120	37.3797	40.0553
130	40.9522	43.6098
140	44.5207	47.1636
150	48.0862	50.7169

$Γ$	$d_{1}$	$d_{2}$	$d_{3}$	$d_{4}$	$p_{R}^{'}$
10	5.8122	5.6037	46.6328	66.50	93.25
9	5.6856	8.4774	43.8858	66.50	93.50
8	5.6347	11.5478	40.8663	66.50	93.58
7	5.7389	14.8395	37.4704	66.50	93.61
6	6.1697	18.3598	33.5192	66.50	93.18
5	7.3316	22.0346	28.6826	66.50	92.83
4	10.2400	25.4409	22.3679	66.50	92.21
3	17.0022	26.8145	14.2321	66.50	90.92
2	28.6168	22.1249	7.3071	66.50	88.87
1	46.5718	5.7409	5.7360	66.50	87.86

$Γ$	$d_{1}$	$d_{2}$	$d_{3}$	$d_{4}$	$p_{R}^{'}$
10	12.8922	10.4519	80.3886	62.00	97.14
9	12.3973	14.8908	76.4446	62.00	97.33
8	11.9297	19.6608	72.1422	62.00	97.50
7	11.5672	24.8216	67.3441	62.00	97.73
6	11.5022	30.4297	61.8009	62.00	97.81
5	12.2595	36.4739	54.9994	62.00	97.65
4	15.4609	42.5255	45.7464	62.00	97.28
3	25.8538	45.8873	31.9917	62.00	96.46
2	46.3994	38.9538	18.3795	62.00	94.80
1	75.2637	13.9775	14.4916	62.00	93.89

m	$d_{1}$	$d_{2}$	$s$	$s^{'}$	$f_{zoom}^{'}$
−5.0	13.3143	70.1019	−21.6785	14.9054	6.1500
−4.5	17.3872	65.9971	−21.6540	14.9617	6.8053
−4.0	21.7222	61.5110	−21.7916	14.9752	7.6123
−3.5	26.3511	56.5076	−22.2283	14.9130	8.6279
−3.0	31.2885	50.7537	−23.2407	14.7171	9.9395
−2.5	36.4661	43.8135	−25.4331	14.2873	11.6841
−2.0	41.4520	34.8305	−30.2360	13.4815	14.0765
−1.5	44.0293	22.7591	−40.8047	12.4069	17.4073
−1.0	35.8698	12.4099	−58.7811	12.9392	21.6288
−0.5	13.9626	12.9311	−81.6924	11.4139	22.4488

$Γ$	$d_{k}$	$d_{1}$	$d_{2}$	$d_{E}$	$p_{R}^{'}$
10	11.1649	13.3143	70.1019	59.9052	109.7
9	11.1404	17.3872	65.9971	59.9611	109.7
8	11.2780	21.7222	61.5110	59.9748	109.7
7	11.7147	26.3511	56.5076	59.9131	109.7
6	12.7271	31.2885	50.7537	59.7169	109.7
5	14.9195	36.4661	43.8135	59.2871	109.7
4	19.7224	41.4520	34.8305	58.4817	109.7
3	30.2911	44.0293	22.7591	57.4069	109.7
2	48.2675	35.8698	12.4099	57.9392	109.7
1	71.1788	13.9626	12.9311	56.4139	109.7

$f^{'} = f_{2}^{'} = d = 1$
$s_{F^{'}}^{'}$	$f^{'} / 5$	$f^{'} / 4$	$f^{'} / 3$	$f^{'} / 2$
$f_{1}^{'}$	1.2500	1.3333	1.5000	2.0000

$m$	$d_{1}$	$d_{2}$	$s$	$s^{'}$	$f_{zoom}^{'}$
−5.0	9.6963	73.8847	−22.9722	13.4467	5.8824
−4.5	13.9359	69.6529	−22.8944	13.5168	6.5060
−4.0	18.4330	65.0572	−22.9598	13.5168	7.2727
−3.5	23.2133	59.9791	−23.2911	13.5165	8.2353
−3.0	28.2812	54.2237	−24.1320	13.3631	9.4737
−2.5	33.5551	47.4475	−26.0021	12.9953	11.1111
−2.0	38.6265	39.0290	−30.0835	12.2610	13.3333
−1.5	41.7636	28.2347	−38.9458	11.0559	16.3636
−1.0	37.2849	17.7437	−55.1568	9.8146	20.0000
−0.5	22.7443	17.4332	−75.4205	4.4020	20.0000

$Γ$	$d_{k}$	$d_{1}$	$d_{2}$	$d_{E}$	$p_{R}^{'}$
10	11.9824	9.6963	73.8847	58.4481	112.5
9	11.9046	13.9359	69.6529	58.5169	112.5
8	11.9700	18.4330	65.0572	58.5505	112.5
7	12.3013	23.2133	59.9791	58.5165	112.5
6	13.1422	28.2812	54.2237	58.3630	112.5
5	15.0123	33.5551	47.4475	57.9955	112.5
4	19.0937	38.6265	39.0290	57.2610	112.5
3	27.9560	41.7636	28.2347	56.0559	112.5
2	44.1670	37.2849	17.7437	54.8146	112.5
1	64.4307	22.7443	17.4332	49.4020	112.5

$m$	$d_{1}$	$d_{2}$	$s$	$s^{'}$	$f_{zoom}^{'}$
−5.0	9.6963	73.8847	−22.9722	13.4467	5.8824
−4.5	13.9359	69.6529	−22.8944	13.5168	6.5060
−4.0	18.4330	65.0572	−22.9598	13.5168	7.2727
−3.5	23.2133	59.9791	−23.2911	13.5165	8.2353
−3.0	28.2812	54.2237	−24.1320	13.3631	9.4737
−2.5	33.5551	47.4475	−26.0021	12.9953	11.1111
−2.0	38.6265	39.0290	−30.0835	12.2610	13.3333
−1.5	41.7636	28.2347	−38.9458	11.0559	16.3636
−1.0	37.2849	17.7437	−55.1568	9.8146	20.0000
−0.5	22.7443	17.4332	−75.4205	4.4020	20.0000

$Γ$	$d_{k}$	$d_{1}$	$d_{2}$	$d_{E}$	$p_{R}^{'}$
10	11.9824	9.6963	73.8847	58.4481	112.5
9	11.9046	13.9359	69.6529	58.5169	112.5
8	11.9700	18.4330	65.0572	58.5505	112.5
7	12.3013	23.2133	59.9791	58.5165	112.5
6	13.1422	28.2812	54.2237	58.3630	112.5
5	15.0123	33.5551	47.4475	57.9955	112.5
4	19.0937	38.6265	39.0290	57.2610	112.5
3	27.9560	41.7636	28.2347	56.0559	112.5
2	44.1670	37.2849	17.7437	54.8146	112.5
1	64.4307	22.7443	17.4332	49.4020	112.5

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