Aperture pupil stop
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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

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Aperture pupil stop
Aperture Pupil (stop)

Exit Pupil

Entrance Pupil


  • 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




Fraction of solid angle

Amount of light collected

the f-number is defined as

Airy disk
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
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
Chromatic Aberration

  • material usually nblue>nred (normal dispersion)

  • blue reflects more than the red, blue has a closer focus.

Achromatic doublet






  • 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


  • Arises from off-axis object points.

  • The transverse magnification is a function of ray height

  • The resulting pattern is like a comet.


  • 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 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


With distortion


  • 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

Books and software
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