An Analysis and Optimization of Distortion Effect Caused by Pupil Decentering in Optical Gun Scope
Abstract
:1. Introduction
2. Analysis of Pupil-Decentering-Induced Distortion
2.1. Mechanism Analysis
2.2. Distortion Evaluation
3. Distortion Reduction
3.1. Optimization of Ray Aberration
3.2. Optimization of the Value of Δx
3.3. Utilization of Vignetting
3.4. Basic Process for Optimizing the Distortion
4. Practical Application of Optimization Methods
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
f′ | Combined focal length of the gun scope and the human eye |
xi | X-coordinate of the image spot |
θx | Field angle of the object point |
ax | X-directional transverse aberration with respect to the chief ray |
ay | Y-directional transverse aberration with respect to the chief ray |
ex | X-directional deviation between a real image spot and the ideal image point |
xp | Ray’s x-coordinate on the exit pupil plane |
yp | Ray’s y-coordinate on the exit pupil plane |
Fx(xp, yp) | Function expression for the distribution of ex with xp and yp |
D | Effective integration region of the human eye’s pupil for Fx (xp, yp) |
Ex | X-directional deviation of the centroid of image spots |
Ex1 | Ex in pupil centering state |
Ex2 | Ex in pupil decentering state |
Δx | Shift in the x-coordinate of the centroid of the image spots after and before pupil decentering |
Δx− | Δx corresponding to an objebt point with normalized field coordinate of (−0.707, 0.707) |
Δx0 | Δx corresponding to an objebt point with normalized field coordinate of (0, 1) |
Δx+ | Δx corresponding to an objebt point with normalized field coordinate of (0.707, 0.707) |
θ | Local angular coordinate of the sampled point on the exit pupil |
ρ | Local radial coordinate of the sampled point on the exit pupil |
M | Number of samples for θ |
N | Number of samples for ρ |
Me | Effective number of samples for θ |
Ne | Effective number of samples forρ |
m | Sampling sequence number of θ |
n | Sampling sequence number of ρ |
θm | The m’th θ |
ρn | The n’th ρ |
Δθ | Sampling intervals for θ |
Δρ | Sampling intervals for ρ |
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Normalized Field | Ex2 (When Pupil Decentered) | Ex1 (When Pupil Centered) | Δx |
---|---|---|---|
(−0.707, 0.707) | 0.08006 | 0.10045 | Δx− = −0.02039 |
(0, 1) | −0.03342 | 0.00000 | Δx0 = −0.03342 |
(0.707, 0.707) | −0.10711 | −0.10045 | Δx+ = −0.00666 |
Normalized Field | Ex2 (When Pupil Decentered) | Ex1 (When Pupil Centered) | Δx |
---|---|---|---|
(−0.707, 0.707) | 0.05279 | 0.04613 | Δx− = 0.00666 |
(0, 1) | −0.00917 | 0.00000 | Δx0 = −0.00917 |
(0.707, 0.707) | −0.03687 | −0.04613 | Δx+ = 0.00926 |
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Yang, K.; Jin, N.; Yang, D.; Xu, M.; Dong, S. An Analysis and Optimization of Distortion Effect Caused by Pupil Decentering in Optical Gun Scope. Photonics 2024, 11, 995. https://doi.org/10.3390/photonics11110995
Yang K, Jin N, Yang D, Xu M, Dong S. An Analysis and Optimization of Distortion Effect Caused by Pupil Decentering in Optical Gun Scope. Photonics. 2024; 11(11):995. https://doi.org/10.3390/photonics11110995
Chicago/Turabian StyleYang, Kaiyu, Ning Jin, Dan Yang, Man Xu, and Shulin Dong. 2024. "An Analysis and Optimization of Distortion Effect Caused by Pupil Decentering in Optical Gun Scope" Photonics 11, no. 11: 995. https://doi.org/10.3390/photonics11110995
APA StyleYang, K., Jin, N., Yang, D., Xu, M., & Dong, S. (2024). An Analysis and Optimization of Distortion Effect Caused by Pupil Decentering in Optical Gun Scope. Photonics, 11(11), 995. https://doi.org/10.3390/photonics11110995