Just read the April Sky & Telescope. An article on fl of objective lenses gave a formula for color free images (3 times the square of the objective diameter). By dumb luck last week I read in one of my old books that the formula was 5 times the square of the objective diameter. Which is right?
Refractor F.L. for Colorless Image
Started by scottw, 02/25/2004 03:26PM
Posted 02/25/2004 03:26PM
Opening Post
Posted 02/25/2004 03:55PM
#1
Depends on aperture and your own definition of "color free." The larger the aperture, the "slower" the objective needs to be in order to yield similar achromatism (of a smaller achromat). A 60mm f/15 achromat will yield less chroma to the average eye than a 150mm f/15 achromat. To my own eye, a 4-inch f/12 achromat is hardly color free. A 4-inch f/20? Dunno -- never seen one.
My 60mm f/13 achromat fits both "rules" -- with lots of room to spare -- but I don't consider it color free.
Best wishes.
-Dan
My 60mm f/13 achromat fits both "rules" -- with lots of room to spare -- but I don't consider it color free.
Best wishes.
-Dan
Posted 02/26/2004 01:17AM
#2
Neither one. They both state standard for "tolerable" chromatism in achromats, not "color free". The more demanding criterion comes from Conrady, who made an arbitrary (but, of course, educated) decision on how much of blue/red defocus can be tolerated. The less demanding criterion seems to be based on the red/blue blur size at the best focus: three times the Airy disc, which, accidentally or not, nearly coincides with the blur size at 1/4 wave of spherical aberration. Calculation shows that not only blur size, but also energy distribution within it (nearly 80% in the central 1/3 of the blur), nearly coincides with that
of 1/4 wave of s.a. (taking into account eye's color sensitivity). So the f~3D^2 is an approximate equivalent for 1/4 wave of spherical aberration. The f~5D^2 is probably comparable to a 1/7 to 1/8 wave of spherical aberration. It comes to near apo levels.
Of course, this applies to nearly perfectly executed achromats. If actual glass indici deviate from the design requirement, it will result in more chromatism. Also, depending on the kind of color correction, chromatism can be more or less apparent to the eye, without it being significantly different in its effect to the image quality.
of 1/4 wave of s.a. (taking into account eye's color sensitivity). So the f~3D^2 is an approximate equivalent for 1/4 wave of spherical aberration. The f~5D^2 is probably comparable to a 1/7 to 1/8 wave of spherical aberration. It comes to near apo levels.
Of course, this applies to nearly perfectly executed achromats. If actual glass indici deviate from the design requirement, it will result in more chromatism. Also, depending on the kind of color correction, chromatism can be more or less apparent to the eye, without it being significantly different in its effect to the image quality.
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