Abstract
Background. Among the parameters and functions to assess the quality of images formed by optical systems RMS spot diagrams parameter is used. This option is usually defined by beam ray-tracing going through optical system. There is a fundamental ability to regenerate RMS by microphotometry of image of real point light sources. However, the RMS of the image is distorted due to finite size source. The problem is that the separation of RMS components values, which are caused by the parameters of the light source and the optical system aberrations.Objective. The recovery of RMS aberration component based on the results of microphotometry of image of extended source of radiation generated with optical system to be tested.Methods. The mathematical tools polar calculations were used, axial and centrifugal RMS from distribution function of illumination in the image of the extended light source, close to the spot. The calculations of mentioned RMS types are conducted by the radii formulas for moments of inertia that are known in theoretical mechanics. Analogue mass they contain is spatial density of luminous flux in the optical image source. In calculating of RMS the source length is included using Huygens- Steiner theorem.Results. New mathematical observations for calculation of RMS including illumination distribution in the image of light sources are obtained. It was established that RMS of each type is Pythagorean sum of components, one of which is specified by the parameters of the source, and the other by the aberrations of the optical system. According to the results of the regenerated RMS from microphotometry of the image of source and the data on the source parameters aberrational component can be determined in each RMS type.Conclusion. The study confirms the possibility of determining the aberration RMS of the optical system according to the results of microphotometry of image of extended light source. The method allows creating new photoelectrical hardware for measuring distances to objects, and to create new types of ophthalmic devices.
Highlights
Among the parameters and functions to assess the quality of images formed by optical systems RMS spot diagrams parameter is used
Розрахунок RMS щодо зображення однієї осьової елементарної ділянки та розрахунок сумарного моменту від зображень усіх елементарних ділянок, на які розбита поверхня джерела випромінювання, можна показати на прикладі розрахунку значення RMS лише полярного моменту
За результатами фотометрії випромінювальної зони джерела світла або за паспортними данимих про функції яскравості випромінювача відновлюються значення RMSR, RMSXY, RMSX, RMSY з використанням для цього формул (1)−(4), у яких замість функцій освітленості підставляються функції, що описують розподіл яскравості випромінювальної зони (в таблиці також наведені формули розрахунку зазначених RMS для типових розподілів яскравості на поверхні випромінювача)
Summary
Among the parameters and functions to assess the quality of images formed by optical systems RMS spot diagrams parameter is used. The recovery of RMS aberration component based on the results of microphotometry of image of extended source of radiation generated with optical system to be tested. The mathematical tools polar calculations were used, axial and centrifugal RMS from distribution function of illumination in the image of the extended light source, close to the spot. The calculations of mentioned RMS types are conducted by the radii formulas for moments of inertia that are known in theoretical mechanics Analogue mass they contain is spatial density of luminous flux in the optical image source. The study confirms the possibility of determining the aberration RMS of the optical system according to the results of microphotometry of image of extended light source. У зв’язку з цим виникає потреба визначення впливу просторових і фотометричних параметрів джерела світла на значення RMS, що поки є нерозв’язаною в теоретичному плані задачею
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