1. Camera lens vignetting
I have used my Sigma APO 150 mm lens a while now and I'm very satisfied with it. Both when travel and when doing astrophotographing. It's just one detail, I feel it vignett a bit to much in the corner (full frame), in some corner almost 50% at aperture f/4. Before I bought this lens I used a medium format lens, the Pentax SMC 67 165 mm f/2.8.
I bought this Pentax 67 (6x7) medium format lens because of its long back focus and big image circle, it shouldn't vignett very much on a full frame sensor. It handle a sensor (film) up to 60 x 70 mm, very far bigger then todays tiny sensors. But it's an old construction and no APO. The lack of APO was the main reason that I later bought the Sigma APO, and then I also got auto focus. For astrophotographing I can do the focus manually. But I must admit since I started to use the remote control app it's very convenient to focus the lens without touching it, no vibration. These both lenses are aimed to my portable mount Star Adventurer.
The Pentax lens has collected a lot of dust since the last time I used it. I have old data from flat calibration that I can use to compare the vignetting of these two lenses. What I remember it wasn't very much vignetting at Pentax. But the resolution was maybe at least one class down compare to the Sigma APO.
2. Histogram and vignetting
You can already in the histogram see how bad or good the vignetting is of your system, compare these two histograms. They are taken from the CFA file and no bias subtraction has been done yet. It's like a raw file in TIFF format. It is an evenly illuminated white screen that is photographed. In the perfect world all pixels should have the same signal.
These two histograms have been done in the Fitswork tool.
This histogram comes from the Pentax medium format lens with aperture set to f/2.8, fully open. The X-axis scale runs from 0 to 16000, that is the range of the 14-bit ADC that a normal modern DSLR camera has.
The same lens but now with aperture set to f/4.0. A normal lens vignett less when reducing the opening. Note how much more narrow the peaks are compare to when aperture is set to f/2.8. Note: You must have the peaks at the same position on the X-axis to compare this. Narrow and high peaks means that more pixels get the same signal. And that is exactly what this histogram says, narrow peaks less vignetting.
The very narrow grey peak to the left is the bias, in this camera it has a value of 2048, the spread we see in the bottom of it is because of a small difference between ADCs and some noise, static and random, there many ADCs in a CMOS sensor. I'm not sure how they add the bias, could be as simple as an analog reference signal before the ADC.
Note about taking flats:
The color balance, each color should have almost the same signal (level) if the QE is the same for each color. In reality it's not the case, the light source is not perfect white and pixels of different color are not of equal sensitivity because of different wavelengths. In a perfect situation all three colors should line up on top of each other. If the color balance is bad, one color with high signal can be over saturated and another color with low signal can be noisy. Sometimes I use a tinted paper, often pink to cover the lens with, pink color reduce the green light.
When you take flats you should try to have them at half of the max signal. But in a heavily vignetting system these peaks can be very broad and then the signal must be lower to not oversaturate part of the peak, the right side in the histogram. The above flat images could take advantages of more exposure, maybe twice as much.
This is a linear histogram in X-axis, in most DSLR cameras the histogram is logarithmic. To get a histogram to look like this you have to place the signal of the strongest color in the DSLR camera's histogram window all the way to the right but not over the edge. You must use the color histogram to see that none of the colors oversaturate. Then there are sensors that are not linear, they compress the signal at high level, not good for a astro camera. Then lower the signal in the flats so that they don't reach the level were this compression starts.
Here I have written more about flat calibration:
It was problem with the monitor to have an even light from it, nowadays I mostly do it with the T-shirt trick or a tinted paper to get the colors in balance.
3. Analyze of Sigma APO 150 mm f/2.8 vignetting
These two images are taken from a color RGB flat.
This is the Sigma APO 150 mm f/2.8 lens. Aperture set to f/2.8, fully open. The line from one corner to the opposite is where the figures come from at the X-axis in the graph, it has the unit pixel. The Y-axis is the signal along this line. Ideally it should have been a flat line when the lens is light up even from a white paper. But it's not a flat line because the lens is vignetting. The signal strength drops from center to the corners.
Look at the green line close to center, the signal is about 120 at this point. Most left and most right side of the line are two of the corners of the sensor. The green line has fallen to 50 here. 50/120 = 0.41 or 41%, that is very much. My goal is to have at least 70% of the center signal level in the corners.
When the lens aperture is set to f/4 it looks better, that's normal. If we do the same calculation once again with the new figures we get 70/115 = 0.6 or 60%. Still a bit high but usable. If you have 50% you can see it like that you only have half the exposure at the corner and then the Signal / Noise is reduced. Flat calibration don't do anything about the S/N, when it adjust the signal level it also increase the noise. We of course want to have the same S/N quality all over the field, that's why it's to prefer a low vignetting lens.
As a comparison with my new Master flat where I demosaic the RGB image, this is the green 1 channel.
This flat is of higher quality. These figures say 33000 / 65000 = 0.507 or 51%. It's a bit worse then the example above, but this Master flat is much more trusty. If you use this lens with a camera that has a APS-C sensor the vignetting will be much less, you only use the center of the field. The sharp peak on the right side in the histogram comes from the flat top in center of the line graph, many pixels with the same value. As a whole this histogram is much wider then the histogram at top of this page from the Pentax lens because it has much more vignetting.
The scale of X-axis in the histogram is not correct. These flats has been normalized to 1 in center and it's a 32-bit floating point file. Fitswork does something wrong when opening these kind of files, it looks that it multiply the level by 65000 (2^16). It doesn't matter, all calculation will be correct anyway.
These two images are taken from the first green channel in a master flat. I normally demosaic my color images to RGGB and thereafter handle them as three (four, but the green1 and green2 are aligned against each other) monochrome images.
4. Analyze of Pentax SMC 67 165 mm f/2.8 vignetting
This is from old data I found when I used this lens a couple of years ago. Note the scale of Y-axis, it does not start at zero. A calculation give us 1800/2200 = 0.82 or 82%. That means that the signal at the corner have just lost 18% compare to center, it's nothing. If the Y-axis has started at zero it had look more like a flat line. And this is done at fully open aperture, f/2.8. The "SMC" on the lens stands for Super Multi Coating, it's only the later lenses that have this.
It was little strange that when I took new flats I got more vignetting of the new ones. I now know that I must have set the aperture ring to wrong aperture, there is a click stop between each normal stop, and the label on the aperture has only 2.8 and then 5.6, not 4.
Anther measurement of the vignetting, now at aperture f/4. 1900/2050 = 0.92 or 92%, even better. But there is no need to stop down the aperture to get less vignetting when it's already this low, but for the resolution it could be an advantage.
When I stop down the aperture I get this strange dissymmetry, part of the explanation could be that a DSLR camera has a very deep entrance and it's not rotation symmetric, it's rectangular and it block the edge ray. Another problem is the mirror that can cause similar problem. A medium format lens has a very wide light cone. A mirror less camera with a big entrance should perform better with it's shorter back focus. The background above look very uneven but that has to do with that this image is stretched.
5. Analyze of Pentax 6x7 at f/2.8 and at f/4.0
The back ground images above that display the flat image is a bit unclear. I have done it in another way here. I use the AstroImageJ software to do this. One flat image with aperture set to f/2.8 and the other set to f/4.0. I took new flats today with the Canon 6D camera. There is a difference compare to the flats I took with the old Canon 5D camera. But it's not easy to have full control over the light situation and maybe I earlier didn't set the aperture to f/4, instead 4.47, just above.
These two images are taken from the first green channel in a master flat.
The black point is set to 60% of max signal for both. The color table is divided in 16 colors, from 100% to 60%, 2.5% units per color step.
Below the images is the histogram. The f/4 has the signal much more concentrated at high level compare to the f/2.8 setting. Still both setting is very good compare to what you get from an ordinary lens mounted on a full frame camera. The f/4 setting gives almost a perfect flat, about 10% drop in signal at the corners. When you open the aperture it increase the incoming light most in the center and much less in the corners.
Some notes, the white area at top and bottom I think comes from reflections inside the entrance of the camera house. The most bottom red line comes from the mirror vignetting. Later I maybe remove this mirror from the camera to get it to perform better.
Now I can understand that they must had redesigned the lenses when they introduced the SLR camera. To fit a mirror between the lens and the film they must have a very narrow entrance in the camera house, then the lens must have a narrow ray cone. For sure not the optimal in view of optical performance. Leica at that time didn't have SLR design and they had the reputation to have very good lenses.
6. Pentax 67 165 mm lenses mounted on a Canon full frame camera
The Pentax 67 lens is built like a tank and it is nice to be a owner of it. Even better if I can have some use of it.
This is how it looks when mounted on a Canon full frame camera.
This is the adapter, there are two versions of Pentax 67 adapters. The one with only inner bayonet and the more advanced with both inner and outer bayonet. The yellow arrows pointing at two of the outer taps, if they are not there you can't use the adapter to a telephoto lens. The outer bayonet is used for the longer focal lenses, longer then 300 mm focal length. It's a big adapter, inside the adapter there is space enough to mount a 2" filter.
The lens itself is a big chunk of metal.
Looking through the lens is just as to look into a very big hole. The 6x7 format has an image circle of 90 mm, to cover a full frame sensor you only need just 44 mm. It's very over sized, that's one reason why it give almost no vignetting on a full frame sensor.
Wikipedia has more information about the Pentax 6x7 system:
I once rejected this lens because it was to soft. Now I give it a second chance.
I did some test to take photos of the Moon, but immediately I found it was difficult to reach focus at infinity, it's on the limit. I need to shorten the adapter or adjust the infinity focus stop inside the lens. Both of them are complicated to do. When I have solved this problem I come back.
Anyway I don't think this old construction will perform very well about the sharpness. I did some primitive test earlier and it look a bit soft if I compare to my Sigma APO. With my new camera with live view camera there is much easier to get the lens in perfect focus.
Conclusion so far:
There are newer designed medium format lenses with ED lens elements. But modern lenses can normally only be controlled together with its camera. There some Pentax 645 and 67 lenses with ED design, they maybe can be set manually aperture and focus. When using a medium format lens on a modern DSLR camera there must be an adapter between, could be both expensive and complicated. I got problem with the focus at infinity. I just wonder how a Canon 200 f/2.8 L lens will perform about vignetting, they are told to be very good to astrophotographing and all photos that I have seen look very good, all the way out to the corner.
And how about small telescopes, say 350 mm f/5.6 APO flat field design, are they better then high quality lenses? I have hard to believe that, but there are other advantages of a telescope.
Now I'm eager to do a star test with the Pentax lens even if I can't get it to focus perfect at infinity.