Figures of Merit for Optical Systems

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Figures of Merit for Optical Systems

• Optical performance
• Geometric image size
• Rms image diameter
• FWHM
• Fractional encircled energy
• MTF at particular spatial frequencies
• RMSWE (root mean square wavefront error)
• Beam divergence
• Distortion
• Boresight

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Two regimes for imaging systems

• Geometric limit
• Use simple ray trace to determine image quality
• Rms spot size is most common FOM
• Valid for wavefront errors gt 1 l
• Near Diffraction limit
• Must take the wave nature (interference and
  diffraction) into account.
• Valid for wavefront errors lt l/4
• Rms wavefront error is most common FOM

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Aberrations - definitions
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Example Lens layout
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OPD plots (DW vs pupil)
DW OPD gtgt 1 l This system is in the geometric
limit OPD (Optical Path Difference) is not a
useful metric for this system
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Spot diagrams
In software, send a bunch of rays through the
system and see where they intersect the image
plane
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Image quality point sharpness

• Look at the image of points
• In the geometric limit
• rms diameter or radius (half-diameter)
• Easily calculated using raytrace programs by
  tracing a bunch of rays This only makes sense
  for geometric limit
• FWHM
• 80 encircled energy

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Geometric encircled energy EE
80 EE is often used as a threshold
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Modulation Transfer Function

• Rather than using the blur size for image points
  use the contrast reduction for high-frequency
  (small scale) features.
• MTF is plot of contrast (or modulation) vs.
  spatial frequency
• Has nice linear properties system MTF product
  of MTF for subsystems.

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Definition of Modulation
(from Smith 2000)
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Modulation Transfer Function
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Diffraction Limit

• Stop the above system down

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Diffraction Limited MTF
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Transition from Diffraction limit to Geometric
Limit
Diffraction limit
Geometric limit
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Diffraction limited
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OPD lt 1 wave
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Spot diagrams

• Now these are meaningless

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Image size comes from diffraction
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Encircled Energy
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Strehl Ratio
Where s is RMS wavefront error in radians
Where Wrms is RMS wavefront error in µm (assuming
l in µm)
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Effect of focus
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Wavefront error effect of focus
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MTF
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Relate focus to RMSWE

• A shift in focus is equivalent to wavefront error
• where
• Remember diffraction limited, a2 l/4
• Convert to rms

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Distortion
Mapping error for image, measured in , µm/mm, or
simply µm
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