Achromatic systems are the most common type of optical systems. At present, the selection of the designed wavelength band of the achromatic systems is mainly determined by the reception range of the human eyes or the detectors, or by previous experience. In this paper, a more accurate method to determine the designed waveband range of achromatic system is proposed. Firstly, the characteristics of the longitudinal chromatic aberration curve of the achromatic system is analyzed. Secondly, establishing the depth of focus(DOF) and wavelength relationship. The DOF is proportional to the wavelength and the square of working F#. Then, a working position is selected and the defocus amount between the working position and the focal position of each wavelength is calculated. Finally, the maximum allowable waveband range is determined by comparing the defocus amount of each wavelength at the working position with 2 times DOF. The method can be used to analyze the design waveband range of achromatic system, which is valuable for designing and testing of optical systems.
Testing wavefront distortions at the design wavelength is critical for optical system qualification. Existing technologies and methods for measuring transmitted wavefronts typically operate at only a few specific wavelengths. In previous research, we propose a method for estimating the wavefront distortion of an optical transmission system in a broad bandwidth. We establish the relationship between the transmitted wavefront and wavelength, using Zernike fringe coefficients to represent the wavefront. We have also experimentally tested a single lens represents the monochromatic transmission system at four wavelengths with interferometers. The results show the monotonic Zernike-wavelength curves of in 400~1000nm bandwidth can be predicted by fitted Conrady formula with three data points. In this paper, we further test a doublet achromatic lens at five wavelengths with interferometers, and we find most Zernike-wavelength curves of the doublet achromatic lens are still monotonic, which can solved by binomial Conrady formula with two data points. Using three points to fit Conrady formula for part of monotonic curves is the same as using two points to solve binomial Conrady formula. However the Z8- wavelength curve which have an inflection point must solved by Conrady formula with three data points. The experimental results of achromatic system are more representative, it shows that Zernike-wavelength curve of achromatic system can be expressed by Conrady formula. In practice testing, if the wavefronts measuring at different wavelengths are accurate, the wavefront of arbitrarily wavelength in a certain band can be estimated by solving Conrady formula. Our experiment shows that the Conrady formula can represent the dispersion characteristics of some optical systems, especially for achromatic system. And the feasibility of measuring transmitted wavefront in a certain band based on Zernike coefficient is verified. The new method will help to simplify the process of multi-wavelength interferometric measurements.
Near-unstable cavities have been proposed as an enabling technology for future gravitational wave detectors, as their compact structure and large beam spot can reduce the thermal noise floor of the interferometer. These cavities operate close to the edge of geometrical stability, and may be driven into instability via small cavity length perturbations or mirror surface distortions. They are at risk of suffering from problems such as high optical scattering loss and Gaussian mode degeneracy. The well-defined Gaussian beams can also be distorted through their interaction with the small imperfections of the mirror surfaces. These issues have an adverse impact on the detector sensitivity and controllability. In this article an experiment is designed and has been built to investigate the technical hurdles associated with marginally cavities. A near-unstable table-top cavity is built and accurate control achieved through length and alignment control systems. This experiment provides an account of the behavior of the near-unstable cavity. Additionally, the experiment provides an insight into how far cavity parameters can be pushed towards geometrical instability.
Testing wavefront distortions at the design wavelength is critical for optical system qualification. The wavefront aberrations is usually expressed in the Zernike polynomials form. As the available wavelength of the laser is limited, wavefronts of an optical system at only a few wavelengths can be test precisely. We consider the change in wavefront with wavelength is caused by the change in the refractive index of the optical material. In this paper we put forward a method for calibrating transmitted wavefront at any wavelength within certain limits. Transmitted wavefronts can be estimated at any wavelength utilizing the relationship between transmitted wavefront and wavelength. We study the relationship between transmitted wavefront Zernike coefficients and wavelength, and choose the Conrady formula to express the function of Zernike coefficients and wavelengths. Zernike coefficients at any wavelength in a certain range can be calculated by the Conrady formula at three other wavelengths. The transmitted wavefront at a specific wavelength can be fitted. Finally, we verify different kinds of optical systems by this method. The result shows the method is effective for the monochromatic system and the achromatic system, while the apochromatism system is form with special glass. The relationship between of the transmitted wavefront Zernike coefficients and wavelength is more complex.
Conference Committee Involvement (7)
Optical Metrology and Inspection for Industrial Applications XII
11 October 2025 | Beijing, China
Optical Metrology and Inspection for Industrial Applications XI
12 October 2024 | Nantong, Jiangsu, China
Optical Metrology and Inspection for Industrial Applications X
15 October 2023 | Beijing, China
Optical Metrology and Inspection for Industrial Applications IX
5 December 2022 | Online Only, China
Optical Metrology and Inspection for Industrial Applications VIII
11 October 2021 | Nantong, JS, China
Optical Metrology and Inspection for Industrial Applications VII
12 October 2020 | Online Only, China
Optical Metrology and Inspection for Industrial Applications VI
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