The invention provides a method for designing a
focal length instrument of an electrodeless
zoom lens. The method comprises the following steps of designing a free-form surface reflector structure byadopting an optical
system design method, using a Zernike polynomial for representing the
surface shape of the free-form surface, using
ZEMAX software for fitting a polynomial coefficient corresponding to the
focal length of a certain measured lens, and acquiring a
surface shape structure meeting the aberration requirement, then sampling and fitting a series of Zernike polynomial coefficients corresponding to the
focal length ranges from -1000 mm to -2 mm and from 2 mm to 1000 mm, and finally, establishing a micro matrix free-form surface reflector by using the obtained Zernike polynomial, controlling an electric transmission device by using a computer to realize
surface shape scanning of the free-form surface reflector, and outputting a focal length value of the measured lens by using thecomputer when a clear image with the maximum image height is displayed on the CCD. The continuous
zoom measurement range is improved to -1000 mm to -2 mm and 2 mm to 1000 mm; one free-form surface reflector is adopted to replace a plurality of
zoom lenses, so that the
assembly difficulty can be reduced, and stepless zoom can be realized.