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06-18-2017, 09:31 PM - 3 Likes   #1
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K-1 Scale Factors - Arcseconds per pixel for several lenses

I used photos of star fields to determine the scale in arcseconds per pixel for some of my camera lenses attached to my Pentax K-1 camera. For each measurement, I took a few second exposure, generally at ISO 1600 and f/4 or f/5.6 . I used an on-line program to analyze each frame.

Here are my results, all in units of arcseconds per pixel ("/p)

SMC Pentax-FA 20-35mm F4 AL at 20mm - - - - - 49.3 "/p
SMC Pentax-FA 20-35mm F4 AL at 35mm - - - - - 29.2 "/p

SMC Pentax-A 28mm F2.8 - - - - - - - - - - - - - - - - 35.0 "/p

SMC Pentax-M 50mm F1.7 - - - - - - - - - - - - - - - - 19.4 "/p

SMC Pentax-DA 50mm F1.8 - - - - - - - - - - - - - - - 19.6 "/p

SMC Pentax-D FA 100mm F2.8 Macro WR - - - - - 10.2 "/p *

SMC Pentax-DA* 300mm F4 ED [IF] SDM - - - - - - 3.44 "/p

The K-1 has around 205 pixels per millimeter. My old K-5 had around 208 pixels per millimeter. Per my recent posting about expected scale factors, based, among other things, on the number of pixels per millimeter (How to make an a priori estimate of camera image scale, in arcseconds per pixel -, I expected these results to be quite close to what I had determined a few years ago for the K-5 (K5 Scale Factor - Arcseconds per pixel for several lenses - For lenses in common, in fact the results are quite similar.

To address the perennial question here on the Forum about whether an APS-C or full-frame camera is better for e.g. birding, I note that my K-3 has more like 256 pixels per mm, which results in a somewhat smaller (fewer arcseconds per pixel for a given lens) scale factor. For example, with my 300mm lens, the K-3 has around 2.77 arcseconds per pixel - noticeably better than the ~3.4 "/p for the K-5/K-1.

So, it depends. A K-5 and a K-1 will be very nearly equal in terms of resolution per pixel with a given lens, whereas a K-3 will beat them both by about 25% - your bird image will be that much wider in pixel count with a K-3 compared to a K-1 with the same lens.

* I kept getting the “wrong” result for the 100mm macro - I knew from both its focal length, and similar measurements on my K-5 and K-3, about what the scale should be, but I was getting results of around 5.6 a/p. I finally realized that I had left a Kenko 2X TC attached to it when I mounted it on the camera!! (A lot can go wrong when you are working in the dark!) The result given here applies a 1.83 scale factor, determined previously for the TC from solar observations (Magnification Factors for several Kenko Teleconverters on K5 - ).

06-19-2017, 06:49 AM   #2

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Keep in mind that the result will vary depending on how far the measurement is made from the center of field. This is particularly true with ultra-wides where the edge arc-seconds/pixel will be significantly greater since there is more magnification there (for rectilinear lenses - not the case for fish-eye lenses). This is one way of looking at the problem of ultra-wides trailing stars at the edges of astrotracer photos - the sensor is being moved to compensate for a particular lens focal length which can be effectively quite different at the edge of field. Narrower field lenses are more uniform to the edges (though they still effectively have a longer focal length at the edges).

The theoretical angle per pixel can be obtained by dividing the pixel spacing (4.9 microns for the K-1 sensor) by the lens focal length and taking the inverse tangent of that value (which yields degrees). To convert to arc seconds, multiply by 3600. This yields 20.21 arc-seconds/pixel for a 50mm lens, which is pretty close to what you got through actual measurement. This approximation is true regardless of they type of lens (FF or APSC).

Since the pixel density is higher (pixels closer) in the K-3, it would be expected that the angular resolution will be higher, however, it's usually the lens that limits the resolution in these cases rather than the sensor (unless a really good lens is being used). As you said, the K-3 will attain a higher angular resolution from a given lens (relative to the K-1) if that lens can get there to begin with, but at the sacrifice of FF coverage.

It's interesting to see the values you've measured and your technique is pretty clever (so the Kenko TC is a only a 1.83x converter??.

Last edited by Bob 256; 06-19-2017 at 07:25 AM.
06-19-2017, 02:37 PM   #3
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Is it not as simple as just lens field of view divided by the pixel resolution of the sensor? E.g. a lens with 20 ° horizontal field of view on a K-1 (horizontal resolution of 7360px) would have a measurement of 9.8 ″/px. With the caveat that there is some variation due to the sensor being flat (not spherical) and also that lenses are not perfect. But that should be the average.
06-19-2017, 03:30 PM   #4
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QuoteOriginally posted by ajack Quote
Is it not as simple as just lens field of view divided by the pixel resolution of the sensor?
Yes, indeed - but where do you get the lens field of view? And, what does that mean: the diagonal value or across the frame (horizontally or vertical).

In general, If you have other information about your camera and/or sensor, then yes you can simplify the process.

My intent here is to let you start absolutely from scratch, knowing only your lens focal length and the physical size and pixel count of your sensor.

06-19-2017, 04:55 PM   #5
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Lens field of view is published for most (all?) lenses. It's listed in the PF lens database, for example. It's also trivial to calculate with a little trigonometry: horizontal field of view = 2*atan(18/ f) for full frame, 2*atan(14/f). You can use horizontal, vertical, or diagonal FOV, you just need to use the corresponding pixel dimensions.

Not that there's anything wrong with your process, it just seems like a lot more work than necessary.
06-19-2017, 07:41 PM - 1 Like   #6

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I might be wrong, but I think AstroDave's original intent was to show that the APSC sensor in the K-3 is capable of a higher (better) angular resolution than that of the K-1. He was calculating that based on sensor pixel spacing (and measurements of a drifting star).

Field of view is approximately that angular value times the number of pixels in the horizontal, vertical, or diagonal direction, respectively, but as ajack pointed out, that's not an exact figure due to lens distortions (and the fact that pixel spacing at the edge of field correlates to a greater angular value than at the center - much greater in the case of an ultra-wide lens). If the average angular value was used, it would come out correctly, but that isn't what AstroDave determined in his star measurements, however, I don't think his original post had anything to do with field of view.

ajack's last post is the correct way to figure field of view based on a lens's focal length (in mm) and the size of a FF or APSC sensor (the 18 and 14 are half the sensor's horizontal dimension in mm - the K-1's sensor is 35.9mm in width).

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