Coma Aberration of a Lens: With a Computational Example

Optical design software is a powerful tool to get all the metrics of an optical design. Nevertheless, an optical designer also knows how these numbers are computed. This video covers DIY coma calculation for infinite conjugates (e.g. object at infinity) using a YNU spreadsheet. The result is benchmarked against Zemax and against an old-fashioned design equation.
THE SIGN OF COMA: A viewer pointed this out. My naming scheme (positive and negative coma) is backwards from some current textbook authors. Several textbooks name it oppositely, as revealed in this paper: opg.optica.org.... I am using what I (and maybe only I) call the Arizona convention: www.azooptics..... But my rationale is simply this: Cases with positive Seidel coefficient are what I chose to call "positive coma". Cases with negative Seidel coefficient are what I chose to call "negative coma". When the marginal rays focus closer to the optical axis than the chief ray pierce, the Seidel coefficient is positive. So that is why I call that case positive. I have noticed that most textbook authors (and software developers) avoid the naming of positive and negative altogether. I can see why!
Typo in the slide at 6:29. The stop shifted coma has A (the marginal ray invariant), not Abar (the chief ray invariant) in the denominator. The correct expression is S_II*=(Abar*/A)S_I. The slide in the video shows S_II*=(Abar*/Abar)S_I, which is an error. The spreadsheet is fine. It was just a typo in this slide.
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This video is the third in the series on optical ray tracing, beginning with:
Paraxial ray tracing with a YNU spreadsheet • Paraxial Ray Trace Equ...
Calculation of spherical aberration • Computing the Third Or...
A very thorough guide for YNU spreadsheeting, and an important resource to help you work through your own spreadsheet, is the "Pencil of Rays" website www.pencilofra...
Optical Design Playlist: • Optics and Optical Design
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[@stephenremillard1]

I see that I left out at 16:30 a helpful comment that the coma elimination condition of X=0.800 is for this refractive index of the crown glass being used in this calculation. The ideal X for zero coma, as well as minimum spherical, varies a little bit within the range of typical crown refractive indices. This spreadsheet is perfect for finding that optimal value of X for other glass types.

[@stephenremillard1]

A viewer pointed this out. The OP deleted the comment, but it's a very important point. My naming scheme (positive and negative coma) is backwards from some current textbook authors. Several textbooks name it oppositely, as revealed in this paper opg.optica.org/ao/abstract.cfm?URI=ao-27-12-2580. I am using what I (and maybe only I) call the Arizona naming convention: www.azooptics.com/Article.aspx?ArticleID=660. But my rationale is simply this: Cases with positive Seidel coefficient are what I chose to call "positive coma". Cases with negative Seidel coefficient are what I chose to call "negative coma". When the marginal rays focus closer to the optical axis than the chief ray pierce, the Seidel coefficient is positive. So that is why I call that case positive coma. I have noticed that some textbook authors (and software developers) avoid the naming of positive and negative altogether. I can see why! Positive and negative are only names.