Diffraction ring pattern at the focal plane of a spherical lens – axicon doublet

1976 ◽  
Vol 54 (17) ◽  
pp. 1774-1780 ◽  
Author(s):  
Pierre-André Bélanger ◽  
Marc Rioux
Keyword(s):  
Plane Wave ◽  
Laser Beam ◽  
Optical System ◽  
Focal Plane ◽  
Focal Length ◽  
Spherical Lens ◽  
Diffraction Ring ◽  
Fresnel Integral ◽  
Drill Holes

A spherical lens and an axicon are combined to form an optical system producing a ring-shaped focalization pattern. The diameter of the ring in the focal plane depends on the angle of the axicon, on its dielectric index, and on the focal length of the spherical lens. The diffractional analysis of the lens–axicon combination, when illuminated by a plane wave, is presented. In particular, we show that, when the aperture is large, the Kirchhoff–Fresnel integral can be reduced to a known function. A close examination of the function reveals that the diffractional width of the ring is equal to approximately twice the width of the Airy pattern of the lens alone. This type of focalization is well suited for a system where a laser beam is used to drill holes.

scholarly journals Catadioptric Optical System Design of 15-Magnitude Star Sensor with Large Entrance Pupil Diameter

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5501
Author(s):  
Yang Bai ◽  
Jianlin Li ◽  
Rongwei Zha ◽  
Ying Wang ◽  
Guangzhi Lei
Keyword(s):  
Optical System ◽  
Attitude Control ◽  
Pupil Diameter ◽  
Focal Length ◽  
Field Of View ◽  
Star Sensor ◽  
Spherical Lens ◽  
Entrance Pupil ◽  
Secondary Mirror ◽  
Entrance Pupil Diameter

The optical system is one of the core components for star sensors, whose imaging quality directly influences the performance of star sensors for star detection, thereby determining the attitude control accuracy of spacecrafts. Here, we report a new type of optical system with a catadioptric structure and a large entrance pupil diameter for a 15-magnitude star sensor. It consists of an improved Cassegrain system (R-C system), an aperture correction spherical lens group and a field of view correction spherical lens group. By embedding the secondary mirror of the R-C system into the output surface of the negative spherical lens of the aperture correction spherical lens group, the blocking of incident light is eliminated from the secondary mirror holder. After the structure optimization, the catadioptric optical system (COS) had a spectral range of 450 nm–950 nm, an entrance pupil diameter of 250 mm, a half-diagonal field of view of 1.4° and a focal length of 390 mm. By using theoretical calculations and experimental measurements, it was verified that the COS, with the ability to correct astigmatism, lateral color and distortion, can fulfill the detection of 15-magnitude dark stars.

Theory and Errors in Stereo Electron Microscopy

1968 ◽  
Vol 26 ◽  
pp. 336-337
Author(s):  
J. M. Pankratz
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Plane Wave ◽  
Focal Length ◽  
Foil Thickness ◽  
Points Of Interest ◽  
Transmission Electron ◽  
Vertical Spacing ◽  
Illuminating System

It is often desirable in transmission electron microscopy to know the vertical spacing of points of interest within a specimen. However, in order to measure a stereo effect, one must have two pictures of the same area taken from different angles, and one must have also a formula for converting measured differences between corresponding points (parallax) into a height differential.Assume (a) that the impinging beam of electrons can be considered as a plane wave and (b) that the magnification is the same at the top and bottom of the specimen. The first assumption is good when the illuminating system is overfocused. The second assumption (the so-called “perspective error”) is good when the focal length is large (3 x 107Å) in relation to foil thickness (∼103 Å).

Expansion of a Focused Laser Beam in the Turbulent Atmosphere

1971 ◽  
Vol 49 (10) ◽  
pp. 1233-1248 ◽  
Author(s):  
A. D. Varvatsis ◽  
M. I. Sancer
Keyword(s):  
Laser Beam ◽  
Free Space ◽  
Turbulent Atmosphere ◽  
Focal Plane ◽  
Spot Size ◽  
Small Aperture ◽  
Forward Scatter ◽  
Green’S Theorem ◽  
Focused Beams ◽  
Weakly Dependent

This work examines the expansion of a focused laser beam in the turbulent atmosphere. The formulation is based on Green's theorem and the valid assumption that the turbulent atmosphere is a forward-scatter medium for wavelengths of interest (0.6 μ < λ < 11 μ). The main results are: (1) the spot size at the free-space focal plane in the presence of turbulence is independent of the aperture radius, and is only weakly dependent on the wavelength, (2) the focal plane can be significantly shifted for small aperture radii, short wavelengths, and long free-space focal lengths, (3) the effect of the atmosphere is pronounced only close to the free-space focus and very far away, and (4) the turbulent atmosphere has a stronger effect on weakly focused beams rather than strongly focused beams, except very close to the free-space focus, where the effect is more pronounced for strongly focused beams.

Long focal length and large aperture zoom optical system

2021 ◽  
Author(s):  
Wei-jun Chang ◽  
Bo Zhang ◽  
Ge-ping Cao
Keyword(s):  
Optical System ◽  
Focal Length ◽  
Large Aperture

Thermal-induced nonlinearities in rose, linseed, and chamomile oils using continuous wave visible laser beam

2018 ◽  
Vol 96 (2) ◽  
pp. 157-164 ◽  
Author(s):  
H.A. Sultan ◽  
Qusay M.A. Hassan ◽  
H. Bakr ◽  
Ahmed S. Al-Asadi ◽  
D.H. Hashim ◽  
...  
Keyword(s):  
Laser Beam ◽  
Continuous Wave ◽  
Input Power ◽  
Diffraction Ring ◽  
Linear Absorption ◽  
Gaussian Profile ◽  
Diffraction Integral ◽  
Visible Laser ◽  
A Cell ◽  
Kirchhoff Diffraction Integral

Self-diffraction rings or spatial self-phase modulation were observed in rose, linseed, and chamomile oils under 473 nm continuous wave laser irradiation. The measurements were performed by propagating the laser beam through a cell containing each sample. The number of rings as well as diameter of the outer-most ring in each pattern obtained increases monotonically with increasing input power. The diffraction ring patterns are theoretically simulated using Fresnel–Kirchhoff diffraction integral in the case of an optically thin medium. The experimental and simulation results show that when a laser beam with Gaussian profile is transmitted through an oil medium, a series of circular diffraction rings forms in the intensity distribution pattern in the far-field. The nonlinear refractive index, n2, was determined from the number of observed rings and by the Z-scan technique. The results obtained from self-diffraction rings experiment and Z-scan are compared and analyzed for the three different oils. A large value was obtained of the order of n2 = 1.32 × l0−6 cm2/W for chamomile oil using the diffraction ring pattern technique. This large nonlinearity is attributed to a thermal effect resulting from linear absorption. Moreover, the optical limiting characteristics of rose, linseed, and chamomile oils were investigated.

scholarly journals Optical Design of a Shortwave Infrared Dual Camera CASSI Based on Improved Offner-Wynne Imaging Spectrometer

2021 ◽  
Vol 2112 (1) ◽  
pp. 012021
Author(s):  
Chong Song ◽  
Lipeng Huo ◽  
Yong Huang ◽  
Yangdong Yan ◽  
Gang Wang ◽  
...  
Keyword(s):  
Optical System ◽  
Imaging System ◽  
Optical Measurement ◽  
Focal Length ◽  
Optical Design ◽  
Optical Transmittance ◽  
Coded Aperture ◽  
Visual Axis ◽  
Imaging Spectrometer ◽  
Shortwave Infrared

Abstract Based on the optical system characteristics of coded aperture snapshot spectral imager (CASSI), an optimized optical system of shortwave infrared dual camera CASSI was designed based on improved Offner-Wynne imaging spectrometer. The operating wavelength of the optical system ranges from 900nm to 1700nm, and the focal length is 1200mm. It consists of two parts: the two dimensional imaging system and the multispectral CASSI imaging system. The key technical parameters of the two parts are the same and there is no visual axis difference. Therefore, the optimized optical system can effectively improve real-time performance, optical transmittance and compactness of the dual camera shortwave infrared CASSI, which is conducive to the application in optical measurement scenes in the shooting range.

scholarly journals A proposed Mathematical Expression for Computer Design of Electrostatic Mirror

2012 ◽  
Vol 9 (1) ◽  
pp. 148-152
Author(s):  
Baghdad Science Journal
Keyword(s):  
Optical System ◽  
Focal Length ◽  
Mathematical Expression ◽  
Optical Element ◽  
Chromatic Aberration ◽  
Computer Design ◽  
Computational Investigation ◽  
Beam Path ◽  
Runge Kutta Method ◽  
Electrostatic Mirror

A computational investigation has been carried out on the design and properties of the electrostatic mirror. In this research, we suggest a mathematical expression to represent the axial potential of an electrostatic mirror. The electron beam path under zero magnification condition had been investigated as mirror trajectory with the aid of fourth – order – Runge – Kutta method. The spherical and chromatic aberration coefficients of mirror has computed and normalized in terms of the focal length. The choice of the mirror depends on the operational requirements, i.e. each optical element in optical system has suffer from the chromatic aberration, for this case, it is use to operate the mirror in optical system at various values of chromatic aberration to correct it in that system.

Statistical characteristics of the speckle images of a scattered laser beam in the focal plane of a receiver objective

2012 ◽  
Vol 79 (9) ◽  
pp. 545
Author(s):  
M. S. Egorov ◽  
S. V. Asanov ◽  
A. B. Ignatiev ◽  
Yu. A. Rezunkov ◽  
V. P. Savelyeva ◽  
...  
Keyword(s):  
Laser Beam ◽  
Focal Plane ◽  
Statistical Characteristics
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