4. Diffraction Limited Metrics

Written by Scott Sparrold

Diffraction Limited Spot Diameter










λ/4 Depth of Focus

In reality no system can be perfectly "focused". There are aberrations to balance. Are you interested in minimum geometric spot diameter? RMS spot diameter? Peak to valley wavefront? RMS wavefront. There are many metrics for setting focus and one usually minimizes some performance metric.

Optical performance will always be "reduced" by diffraction. In other words diffraction will cause image degradation. Lord Rayleigh has stated that if an optical beam has less than a quarter wave error, it is as good as diffraction limited performance. This is called the "Rayleigh Criteria". Therefore quarter wave error is a metric to shoot for.... why reduce or balance your aberrations any lower if diffraction is ever present.

When focusing a beam, therefore, the optical engineer needs a good intuitive understanding for how good it needs to be focused:


where
F/# = the f-number or effective focal length divided by the entrance pupil diameter
λ = the center wavelength

Example. An F/5 system operated in the visible (λ = 587 nm) the quarter wave depth of focus is ±29µm. 
  • This tells the opto-mech engineer that he doesn't need to design a focus stage that has a resolution better than 29µm.
  • It tells the optics engineer worried about thermal defocus that he doesn't need to worry about changes less than ±29µm. 
  • It tells the end user who is imaging a depth of field (in object space) that his image space focus can move ±29µm before it goes out of focus. To convert from image space to object space defocus range one must use longitudinal magnification, which is lateral magnification squared (link and description to be added later)