Frequency analysis of optical imaging system Dinesh Ganotra

Imaging System

Lens Design Software Effective Focal Length Max. Field Angle Stop Surface Number Afocal EFL Back Focal Length Zoom Surface Working Distance Wavelength (Primary) No. of Zoom Positions Telephoto Ratio Refractive Index (Primary) Overall Physical Length Abbe Number Entrance Pupil Diameter No. of Glass Elements Max. Parax Image Height Overall Glass Length Lateral Magnification No. of Optical Surfaces Angular Magnification No. of Physical Surfaces Zoom Ratio No. of Cemented Groups Numerical Aperture Number of Examples

Imaging system   v u zozo zizi

Point Spread

Geometrical optics  Diffraction optics : image amplitude : amplitude at image coordinates in response to a point source object at Amplitude point spread function

Amplitude Point Spread Function : Pupil function : unity inside and zero outside the projection aperture. Superposition integral

MTF PSF

Reduced coordinates ; Ideal image

Amplitude PSF in reduced coordinates

Diffraction limited system regard the image as being a convolution of the image predicted by geometrical optics with an impulse response that is the Fraunhofer diffraction pattern of the exit pupil.

Spatial coherence where  is the time delay associated with propagation from to in general,  is a function of the coordinates involved.

Intensity

Drop time delays where known as mutual intensity.

Take time-varying phasor at the origin as reference For a perfectly coherent illumination Thus

Coherent object illumination is linear in complex amplitude

Frequency response Coherent illumination Incoherent illumination

Coherent illumination Define Amplitude transfer function Fourier transform of PSF

Coherent imaging … Taking Fourier transform on both the sides and using convolution theorem

Substituting h(u,v)‏ Take and ignore negative signs

Cut off frequency Example = cm w=1 cm z i = 10cm give cut off frequency of 100 cycles / mm

Incoherent illumination Convolution of intensity impulse response with ideal image intensity

Define

Take FT on both sides and use convolution theorem Optical transfer function

Relationship between OTF and amplitude transfer function Amplitude Transfer Function Point Spread Function Optical Transfer Function OTF is normalized autocorrelation function of amplitude transfer function

Why frequency analysis?