Theoretical treatment of lens design tradeoffs?

<p>There doesn't appear to be a more appropriate forum for this question, though it may not be on-topic for this forum either.<br>

I'm looking for material presenting a theoretically oriented treatment of the tradeoffs and design decisions in photographic lenses. The Wikipedia article is interesting as far as it goes, but I'm looking for greater depth. My background is quite technical (I have a degree in physics) but I've not studied the field before, so I'm not afraid of complexity as long as the material lays the groundwork too.<br>

Things I'd like to understand better are:<br>

- why is it hard to make high-aperture wide-angle lenses? (for telephoto lenses the reasons are obvious)<br>

- what other things get sacrificed to achieve flatness of field?<br>

- what are the effects of moving the diaphragm to different locations in the lens?<br>

- what generates coma? How does one avoid it? <br>

- why do some lenses have focal lengths that vary with subject distances?<br>

- if I want to modify a design to reduce minimum focus distance, what will I need to compromise to do so?</p>

<p>I'm not actually seeking to do lens design myself, I'd just like to understand the challenges and trade-offs more.</p>

 

<p>Check out <a href="http://books.google.com/books?id=7qCtsFeF7lkC&dq=kingslake+lens+design+fundamentals&printsec=frontcover&source=bl&ots=eJ0rzS5ff4&sig=JjbMccpXwECOiIpJZQdTrSeAYVU&hl=en&ei=CdEbS_mBF4X0Mb_Z8ecC&sa=X&oi=book_result&ct=result&resnum=3&ved=0CBUQ6AEwAg#v=onepage&q=&f=false">this book</a> for a start. It probably does not have the answers to all your questions though.</p>

<p>Study some books by A. E. Conrady; Rudolf Kingslake; Warren Smith; ; and study classical len designs first. Then dabble into computer lens design; optical glass types.</p>

<p>Wanting a great fast wide angle that is low in cost is like wanting a women that is super pretty; makes a million bucks; wants 5 kids; can bake biscuits at 3am; requires zero sleep; and is tolerant of all mans monkey business.</p>

<p>Lens design is very complex and deep subject. It is ancient too. The lay public often has no clue on the tradeoffs involved.<br>

<br /> Moving the diaphram around changes alot of things when off axis; even with a simple one element lens like in an old box camera.<br>

<br /> On this old cumputer here a Pentium III with OSLO EDU; one has more optical computing power in a 1 hours session than would take a decade of a dozen men in the 1940's to compute. Back then a *computer* was a persons job title.<br>

<br /> One of the first lens designed with a electronic computer was the 80mm F2.8 Xenotar back in about 1952; a Swiss computer was used.</p>

<p>In the 1970's computer costs dropped rapidly and many older lens designs were just made more produceable via tolerance analysis.</p>

<p>You might want to check out some of the books I list here - <a href="http://www.bobatkins.com/photography/technical/mtf/mtf6.html">http://www.bobatkins.com/photography/technical/mtf/mtf6.html</a></p>

<p>"Modern Optical Engineering" by Warren J. Smith might be a good start. You can usually find used copies for a few dollars since it was used as a college textbook. His "Modern Lens Design" is also worth looking at.</p>

<p>There's also "Aberration Theory made Simple" by Virendra Mahajan. The word "Simple" here is a relative term.</p>

<p>Most abberations grow worse going off axis; often with the square or cube of the arc angle.<br>

<br /> Most abberations grow worse with a faster f-stop.<br>

<br /> Thus *wanting* a great fast wide angle lens wide open is big compromise.<br>

<br /> Its like wanting an 80 year old quarterback that gets 2 hours of sleep per night to throw perfectly; over long distances to a moving receiver.<br>

<br /> Most lenses have spherical surfaces; they are easy to make; easy to check. God/nature does not naturally make aspherical lenses by grinding. Asphericals are used in cellphones; then are molded or shaped.<br>

<br /> Vigneting is PURPOSELY introduced in wide angle lens designs to cut off ill rays. One makes the corners sharper; but illumination is dropped. IF the lens was for a low resolution security camera; then maybe one would steer the design more towards filling the corners. The lay public often thinks vigneting is bad; when it is a purposely used TOOL in lens design; sort of like a spam filter; one gets less mail but more focused on what you want.<br>

<br /> With optical glass what is available has grown over the last several decades. At any point in history the new stuff costs alot more; maybe 10 to 1000 times more per pound of glass. One balances several different lens types to reduce color errors.<br>

<br /> Before lens coatings arrived in the mid to late 1930's; all lenses were not coated. Each uncoated surface with an air interface would have a 4 percent loss. Thus prior to World War 2 many complex lens designs were known; but not used much. The Triplet and Tessar ruled the roost. Kodak started to coat lenses between 1939 to 1940 and used it in high end stuff.<br>

<br /> Even a lens like the common 50mm F2 non a 35mm still camera are still refined; and then have been around for over 7 decades.</p>

<p>As BOB mentioned; ""Modern Optical Engineering" by Warren J. Smith is a GREAT textbook.<br>

<br /> It is in its 4th edition now. Here I have older edtions; first was back in 1966. Warren taught Optical design in the University of Wisconsin extension courses in Madison, Wis; or would go to your company if the group was large enough. I took a couple of his courses; one in Madison; another in SoCal at a place I worked. Warren was at Infrared Industries in Carpenteria Calif between Ventura and Santa Barbara; I interviewed there once long ago. Warren wrote one of Mil Handbooks on optics. Warren passed away in June 2008; his whole life was in optics; a very great man. He was a OSA member for 65 years; and in SPIE too. We was a great teacher. He was involved in lens design be computers when they had vacuum tubes.<br>

<br /> Rudolf Kinglake wrote several excellent books; he passed away several years ago; another great legend. His optical design books are classics.<br>

<br /> Optical design is subject that the more learns; one discovers one really knows a lessor percentage of what is out there.</p>

<p>There is a inexpensive reprint of A.E Conrady's " Applied Optcis and Optical Design" that is in paperback by Dover c 1960, 1988 that has alot of info. He was great German lens designer from 1866 to 1944. He lived in England after about 1900. His son in law is Rudolf Kingslake; the guy who drove Kodak Rochester lens dept in the late 1930's and later.</p>

<p>- why is it hard to make high-aperture wide-angle lenses? (for telephoto lenses the reasons are obvious)<br>

For view cameras and rangefinder cameras. this is not so much of a challenge because the lens can be made symmetrical. In the SLR, the front group must be very negative to be able to be combined with a very positve rear group to allow for the clearance of the mirror box. As a result, the diameter of the negative group must be huge to attain any speed. Most of the rays from the negative front group are not imaged at the focal plane, but are lost in the baffeling due to the fact that the rays are highly diverging. The wider the view, the more divergent the rays in the front group. Slightly wide lens can be made quite fast without too much problem. The super wides become a major problem. The diameter of the front element becomes too large to make an economically viable lens. The fairly slow 55mm f/3.5 Pentax lens for their 6x7 had a 100mm filter. Going beyond that diameter would not be realistic.<br>

<br />- what other things get sacrificed to achieve flatness of field?<br>

AKA Curvature of field- The flatness of the focal plane is really not that much of a constraint in designs. In many lenses, especially telephotos, a negative element is added in the rear to flatten the field. However in more modern designs, the field is flattened as a part of the entire formula, not just as an after thought with a field flattener. Sacrifices are not needed.<br>

<br />- what are the effects of moving the diaphragm to different locations in the lens?<br>

The major problem with doing that, is vignetting of the image by the diaphragm.<br>

<br />- what generates coma? How does one avoid it? COMA is an oblique aberration that can be eliminated by using symmetrical designs.<br>

<br />- why do some lenses have focal lengths that vary with subject distances?<br>

This has to do with the angle of the rays entering the optic. At macro distances, the rays are diverging when entering the lens and thus cause the image to be focused further back. At infinity, the rays are parallel and therefore focus shorter. It is easier to see this in a graphical display, not so easy to put into words.<br>

<br />- if I want to modify a design to reduce minimum focus distance, what will I need to compromise to do so?<br>

Spherical aberration is the major consideration addressed when close focusing is required along with infinity work. Floating elements are the most common solution to this, especially in wide lenses. The 45mm lens for the Pentax 67 is a classic example but there are many more. Many macro lenses use this technique as well for infinity performance, as well as close work. So spherical correctness is not sacrificed when using a floating element.</p>

<p>Check out <a href="http://en.leica-camera.com/assets/file/download.php?filename=file_1754.pdf">this pdf</a>.</p>

 

<p>It's about Leica glass, but the first few chapters outline very well the different obstacles and trade-offs a lens designer has to make.</p>