Aperture Pupil (stop)

1. Aperture Pupil (stop) Exit Pupil Entrance Pupil

2. 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

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

4. 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

5. 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.

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

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

8. 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

9. 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

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

11. 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.

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

13. 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

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

15. Ray-tracing and computer-aided design

16. Books and software • Software • 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