Chromatic focal shift of optical system expressed by related wavelength formulas

Chromatic focal shift is used to characterize the variation of focal wavelength of optical system with wavelength. It is an important tool and index to analyze the color difference of optical system. In this paper, the function relationship between focal length and wavelength of optical system is analyzed by using chromatic focal shift. According to the dispersion characteristics of the optical system material, the Conrady formula which fits the refractive index curve well with less data is selected. Simulations show that the chromatic focal shift of most of monochromatic wavelength systems in the 400-1000 nm wavelength range is monotonically increasing and can be expressed by the Conrady dispersion formula. The chromatic focal shift of achromatic systems which consists of a variety of glass materials usually has an inflection point, and the shapes of most of the achromatic chromatic focal shift are the same, so the formula for the curve should be consistent.The calculation results show that the Conrady formula can also solve the curve of the achromatic system effectively in a relatively short band, such as 400nm~700nm. In fact, the chromatic aberration correction of most achromatic systems is limited, and the effective working band is short. Therefore, the Conrady formula is a very good expression for both monochrome and achromatic systems. By studying the chromatic focal shift analytical equation of the optical system, it provides a reference for the theoretical calculation and detection of focal length at a specific wavelength.