Aperture Pupil (stop) Exit Pupil Entrance Pupil

Telescope The entrance pupil often is the entrance lens diameter (most expensive/difficult-to-fabricate element) Magnifying the angle of the incident light The Exit pupil should match the field of view of eye Light collection capability depends on the size of entrance pupil

F-number D f Fraction of solid angle Amount of light collected the f-number is defined as

Airy Disk The actual spot size is not a dot, as described by ray optics The ring of airy disk is due to diffraction (wave property) The diameter of airy disk cannot be smaller than the wavelength of light

Aberrations: chromatic and monochromatic Chromatic aberrations: n=n(w) rays corresponding to different wavelengths travel different paths Monochromatic aberrations: image is blurred or deformed due to the approximation error in the paraxial approximation to the exact solution.

Chromatic Aberration material usually nblue>nred (normal dispersion) blue reflects more than the red, blue has a closer focus.

Achromatic doublet R2 R1 R3 n1 n2 Achromatic doublet (achormat) is often used to compensate for the chromatic aberration the focuses for red and blue is the same if

Monochromatic Aberration Monochromatic aberration is due to the paraxial rays are just an approximation to the real case. For paraxial approximation, we assume but actually The second term are called the third-order correction to the first order theory (or first-order corrections to the paraxial theory) The third order corrections are Spherical aberration coma astigmatism field curvature distortion

Spherical Aberration Spherical aberration comes from the spherical surface of a lens The further away the rays from the lens center, the bigger the error is. The image is improved if the image plane move closer to the lens to find optimal spot size

Coma Arises from off-axis object points. The transverse magnification is a function of ray height The resulting pattern is like a comet.

Astigmatism In optical design, the vertical plane is general called the “tangential plane” The “sagittal plane” is the plane at right angle to the trangential plane and containing the principle ray. Astigmatism results in different focusing power to the tangential and sagittal plane.

Astigmatism tangential sagittal Astigmatism often arises when focusing with a mirror with an angle

Field Curvature Object plane Image plane a thin lens image a spherical surface onto a spherical surface therefore, image is distorted in the image plane important in lens design for close objects

Distortion With distortion Corrected all points in the object plane are imaged to points in image plane Distortion arises when he magnification of off-axis image is a function of the distance to the lens center

Ray-tracing and computer-aided design

Books and software Software Book Zemax (http://www.zemax.com) Code V by Optical Research Associates (http://www.opticalres.com/) Book The Art and Science of Optical Design, R. R. Shannon, Cambridge 1997