This is a continuation of testing of the following macro lenses :
- Sony 90mm f/2.8 FE Macro
- Leica 100mm f/2.8 Apo Macro-Elmarit-R
- Zeiss 100mm f/2 Makro-Planar ZF
- Nikon 105mm f/2.8 Micro-Nikkor G VR
The test starts here:
There have been questions about what I’m really measuring with my longitudinal chromatic aberration (LoCA) tests, and I’d like to deal with them as best I can in this post.
First off, a word about my test methods in general.
When I was going to Stanford in the early 60s, there were two introductory physics tracks. One, which was intended for people who intended to graduate in science or engineering, assumed a knowledge of calculus. The other, intended for liberal arts majors and others (including a lot of pre-meds!) who just wanted to get a little deeper into physics than a typical high school course, danced around the physics things that needed calculus to properly explore. Everybody – not just the techies – called the non-calculus version “kitchen physics”.
What I do on this blog is analogous to kitchen physics with respect to equipment. I neither possess or know how to use the gear that camera and lens designers use for testing. I couldn’t afford a $200,000 optical bench, wouldn’t have a place to put it, and wouldn’t be able to operate it if I did. I try to do the most I can with normal photographic equipment, just like the folks in kitchen physics did with algebra and trig. I may throw in an oscilloscope and a motorized focusing rail from time to time, and do some computer programming that would be outside the comfort zone of many photographers, but my objective here is to see how much I can discover with tools that might be found around the house of a serious photographer.
So let’s call the LoCA work that I’ve been doing “kitchen optics.”
If you’re unclear on the procedure I’m using, take a look at this:
There are things in physics that are simple to explain, and even elegant, that get a bit messy when you don’t have calculus in your toolkit. “S equals ut plus half a t squared, but just trust me on the derivation of that.” Versus “a is the second derivative of s with respect to t” Turns out that there are things in kitchen optics that aren’t as straightforward as they would be if you had an optical bench at your disposal.
So bear with me while I work through my reasoning on my LoCA test. In addition, if you happen to be an optics expert – which I am most assuredly not – and you find an error, I’d appreciate it if you’d bring it to my attention.
Let’s go back to the definition of LoCA. Wikipedia says:
“Axial aberration occurs when different wavelengths of light are focused at different distances from the lens, i.e., different points on the optical axis (focus shift).”
Axial aberration is another name for LoCA.
So, since I don’t have a real optical bench, and presumably neither do you, let’s conjure up an imaginary one and do a thought experiment.
First off, the classic version. Assume a collimator that allows perfectly parallel light to impinge upon the lens. With a lens free of LoCA, and otherwise perfect, all that light would be brought to a focus along the lens axis, at a distance of the focal length from the center of a hypothetical single element with the same focal length (feel free to ignore that last bit, which was included in a probably unwise attempt at not oversimplifying). Anyway, all the light comes to a focus at one point. If we take an on-axis energy probe on our imaginary optical bench, the ready goes up as we approach the focal point from either side, and reads the entire energy of the light beam at the focal point. If we replace the energy probe with a spectrophotometer, the spectrum at the focal point is the spectrum of the light beam itself.
Now let’s replace the perfect lens with one that is equally perfect in every way except, when 550 nm (greenish) light is focused in the nominal focal plane, 450 nm (blueish) light is focused 1 mm closer to the lens, and 650 nm (reddish) light is focused 1 mm farther away from the lens. If we move our probe along the axis of the lens, we will see three peaks, not one. If we use our spectrophotometer, we’ll see that the peak furthest away from the lens is almost all 650 nm light (with a little of each of the other wavelengths from out-of-focus blurs). The middle peak will be almost all green light, and the near one almost entirely blue light.
If we add diffraction to the lens, then the peaks get broader and less high, with the blue peak being the most affected, the green the next, and the red the least.
Now, let’s do away with the collimator, and put an on-axis point light source at twice the focal length in front of an ideal, no-LoCA, lens. When we probe behind the lens, we will find a peak at twice the focal length behind the lens, and the spectrum of the peak will be the same as the spectrum of the light source.
Now let’s put LoCA and diffraction into the lens, and use our three-wavelength light source as above. If we use the spectrophotometer, we’ll see that the peak furthest away from the lens is almost all 650 nm light (with a little of each of the other wavelengths from out-of-focus blurs. About 2mm towards the lens, we’ll find middle peak, which will be almost all green light, and 2 mm further on, we’ll see the nearest peak to the lens, which is almost entirely blue light.
OK, we’re done with the imaginary optical bench. Now we’ll put the lens on an imaginary digital camera, which has a Bayer color filter array (CFA). Let’s say the red part of the CFA responds mainly to 650 nm light, the green part mainly to 550 nm, and the blue to 450 nm. If we rack the lens in and out while taking pictures all the while, we’ll see the central red pixel in the CFA peak in intensity with the lens farthest from the sensor, the central green pixel in the CFA peak in intensity with the lens at a middle distance, and the central blue pixel in the CFA peak in intensity with the lens closest tp the sensor. This is almost, but not quite, what we did when we probed the on-axis behavior on our imaginary optical bench. The difference is that with the camera, moving the lens gets it farther from the sensor and closer to the subject, so the magnification changes, and the relationship of the readings won’t be quite the same as with the bench.
There’s only one more thing we need to do to our imaginary camera to reproduce the situation that I’m using for the LoCA testing. Instead of changing the focus by racking the lens back and forth, which I don’t know how to do precisely in real life, we will change the focus by moving the camera back and forth along the lens axis.
The difference in the three focusing modes: changing the position of the probe, changing the position of the lens, and changing the position of the camera, is to stretch or squeeze the distance axis somewhat, in a nonlinear, but monotonic fashion. Therefore, the curves that we get from all three ways of focusing will look similar to one another, but they won’t be identical.
In all cases, the curves from a lens with no LoCA will peak at the same place. In all cases the sharper the focus achieved, the narrower and higher the peaks. In all cases, the distance between the peaks is a measure of LoCA.
Not quite. In my LoCA test, I don’t measure light intensity at a single pixel as an indication of degree of focus. There would be too much noise if I did that. Instead, I used slanted edge MTF50 as a stand-in for intensity. I can get much more accuracy that way.
And, if you accept that last tweak, then, yes, QE(approximately)D.
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