01-21-2015, 05:46 PM
There are many aspects to lens design which would baffle most photographers. In general the optics industry really does not care what photographers want for lenses on a "quality" note. For example, photographers would love a lens that is completely transparent and has no meaningful aberrations of any kind and such a lens can be designed, but no one could pay for it if it were fast.
Designing lenses is a balancing act and a compromise between the various aberrations and it takes a great deal of skill to get to a good result and often things are rounded. For example, nikon's 50mm f/1.8G is really closer to being f/2 wide open. The first commercial lens to ever feature an asphere was "f/1.2" but the manufacturing specs would only support f/1.4 -- the rays for f/1.2 are mechanically cut off. I would state with a great deal of confidence that if the transmission of the 135/1.8 is under t/2.2 the lens is f/2 at best and not actually f/1.8 as well.
Anyway, in simplest terms distortion results from an uneven distribution of power around the aperture stop. The double gauss design form corrects distortion through symmetry which is why it is uncommon to see high distortion fast 50s. The sonnar form, which most faster lenses over 85mm use, solves for distortion by placing a negative element before the aperture stop to reduce the power of the lens before the stop and meet it with mild power behind the stop. The result is lowish distortion and is fairly brilliant. The radii of curvature in front of the stop on a couple surfaces are very low, so there are massive aberrations there. By making the lens longer and splitting elements the designs are improved to a usable level.
If you fix distortion by moving the stop, you entirely redefine the corner performance of the lens - the chief ray which defines the image circle is pointed at the aperture stop... if you move it the chief ray moves with it. Aspherical elements will also add "wiggle" to the distortion which there is no mechanism for correcting.
Field curvature (hence forth referred to as petzval) is the source swirly bokeh. Add a little vignetting and you have the complete formula for it. If you consider a single lens, it will be free of lower order petzval and reasonably free of higher order petzval if the curvature of the first surface is equal and opposite to the curvature of the second element. If these elements are split and compounded several times you get symmetric design forms like the biotar or double gauss or landscape lens, etc. These designs have a flat field through symmetry as well - if the "net refractive index" of the front half does not equal the back half behind the stop, you get an uneven distribution of power about the stop even if the curvatures match. This produces distortion.
Weighting the optimizer and guiding it is also a balancing act. Typical color weighting is red+blue=1 each, green=2 to mimic the eye. Weighting center vs corner depends what you are trying to accomplish. But for example, "no coma" would mean weight the corner strongly. I believe samyang does this and in general due to their size I think they "have a thumb" on the photographic community's wants more than bigger designers.
But bigger 'design centers' attend industry events, read JOSA and SPIE publications, talk with industry members, and so on and so forth. Never do the desires of photographers re: aberration balance come into the question.
https://dl.dropboxusercontent.com/u/3928...Design.pdf
Here is an article that predates CAD that is somewhat relevant- it is about the implementation of computers into the design of lenses and how the process works (or worked, but things have not changed too much in that regard).
Many commonplace things today are referenced in their infancy in this one. 'frequency response' is the thought or idea that grew into MTF, and the diagrams of methods of interferometric testing have become commonplace within optics. Particularly figure 4 has seen almost no change but is now known as a Fizeau interferometer.
Note that the target for the hypothetical lens is not even in terms that photographers would use. Part of that is the historical nature of the article, but things are still done that way. Depending on the background of the lead designer you design for a certain amount of wavefront error in waves, or you design for a certain MTF value (usually > 50% across the field at the nyquist of the sensor is the goal) or you design for a certain spot size (usually on the order of a pixel in rms diameter) or you design for the RIM plot to nicely fit in a certain scale, for example.
Designing lenses is a balancing act and a compromise between the various aberrations and it takes a great deal of skill to get to a good result and often things are rounded. For example, nikon's 50mm f/1.8G is really closer to being f/2 wide open. The first commercial lens to ever feature an asphere was "f/1.2" but the manufacturing specs would only support f/1.4 -- the rays for f/1.2 are mechanically cut off. I would state with a great deal of confidence that if the transmission of the 135/1.8 is under t/2.2 the lens is f/2 at best and not actually f/1.8 as well.
Anyway, in simplest terms distortion results from an uneven distribution of power around the aperture stop. The double gauss design form corrects distortion through symmetry which is why it is uncommon to see high distortion fast 50s. The sonnar form, which most faster lenses over 85mm use, solves for distortion by placing a negative element before the aperture stop to reduce the power of the lens before the stop and meet it with mild power behind the stop. The result is lowish distortion and is fairly brilliant. The radii of curvature in front of the stop on a couple surfaces are very low, so there are massive aberrations there. By making the lens longer and splitting elements the designs are improved to a usable level.
If you fix distortion by moving the stop, you entirely redefine the corner performance of the lens - the chief ray which defines the image circle is pointed at the aperture stop... if you move it the chief ray moves with it. Aspherical elements will also add "wiggle" to the distortion which there is no mechanism for correcting.
Field curvature (hence forth referred to as petzval) is the source swirly bokeh. Add a little vignetting and you have the complete formula for it. If you consider a single lens, it will be free of lower order petzval and reasonably free of higher order petzval if the curvature of the first surface is equal and opposite to the curvature of the second element. If these elements are split and compounded several times you get symmetric design forms like the biotar or double gauss or landscape lens, etc. These designs have a flat field through symmetry as well - if the "net refractive index" of the front half does not equal the back half behind the stop, you get an uneven distribution of power about the stop even if the curvatures match. This produces distortion.
Weighting the optimizer and guiding it is also a balancing act. Typical color weighting is red+blue=1 each, green=2 to mimic the eye. Weighting center vs corner depends what you are trying to accomplish. But for example, "no coma" would mean weight the corner strongly. I believe samyang does this and in general due to their size I think they "have a thumb" on the photographic community's wants more than bigger designers.
But bigger 'design centers' attend industry events, read JOSA and SPIE publications, talk with industry members, and so on and so forth. Never do the desires of photographers re: aberration balance come into the question.
https://dl.dropboxusercontent.com/u/3928...Design.pdf
Here is an article that predates CAD that is somewhat relevant- it is about the implementation of computers into the design of lenses and how the process works (or worked, but things have not changed too much in that regard).
Many commonplace things today are referenced in their infancy in this one. 'frequency response' is the thought or idea that grew into MTF, and the diagrams of methods of interferometric testing have become commonplace within optics. Particularly figure 4 has seen almost no change but is now known as a Fizeau interferometer.
Note that the target for the hypothetical lens is not even in terms that photographers would use. Part of that is the historical nature of the article, but things are still done that way. Depending on the background of the lead designer you design for a certain amount of wavefront error in waves, or you design for a certain MTF value (usually > 50% across the field at the nyquist of the sensor is the goal) or you design for a certain spot size (usually on the order of a pixel in rms diameter) or you design for the RIM plot to nicely fit in a certain scale, for example.