Easy, it is 550 mm. Or is it? While refining my PEC curve (I need the value to convert the measured PE offsets from pixels to arc seconds), I came to ask myself what the effective focal length of my scope really is.
For small angles, the focal length is simply given by:
focal length = pixel pitch / plate scale
The pixel pitch is known from sensor manufacturers, and the plate scale is kindly provided by the plate-solving service of AstroBin
For example, for my latest image (AB-measured plate scale 2.429"/pixel) taken with my EOS 6D (6.54 microns pixels), I get:
F = 555.36 mm
Which is about 1% longer than the listed value. How accurate is this estimate? Pixel pitches are typically given to 0.01 microns, for sizes of about 5 microns. I thus estimate that they are accurate to at least 1e-3. From a few plate solves of my own images, I estimate the error on the plate scale to be of that order also. The 1% extra length found should thus be significant. No big deal, but is this just my copy?
To test this, I used AB to compute focal lengths from a bunch of images taken with ESPRIT 100EDs. With AB's API, I got plate scales for 1220 images taken during the past year, with a variety of cameras: Monos, OSCs & DSLRs. I took the median value for each user (assuming a single copy each), and computed the histogram. This gives the step curve in the graph below:
It is peaked at 555 mm (meaning that my copy is pretty typical), with a dispersion of a few mm. One can check that there is no significant dependence of the focal length with pixel sizes, meaning that uncertainties on these latter are not the source of the dispersion. The pastel-colored curves are histograms for individual users with more than 20 images, which gives an idea of the measurement dispersion for individual copies. There are a few stray values (and several possible causes) but they should not affect the conclusions.
I don't know why the focal length is listed as 550 mm and not 555. One answer could be: "who cares?". Another could be that the focal length of the triplet is indeed 550 and that the field corrector used by all imagers increases the effective length a bit. Or something else.
Anyway, I did this for fun and out of curiosity, and the 1% difference from the nominal has absolutely no importance. But who knows, maybe somebody will care, hence this long post
CS,
Frédéric
PS: AB is really a fantastic resource!
For small angles, the focal length is simply given by:
focal length = pixel pitch / plate scale
The pixel pitch is known from sensor manufacturers, and the plate scale is kindly provided by the plate-solving service of AstroBin
For example, for my latest image (AB-measured plate scale 2.429"/pixel) taken with my EOS 6D (6.54 microns pixels), I get:F = 555.36 mm
Which is about 1% longer than the listed value. How accurate is this estimate? Pixel pitches are typically given to 0.01 microns, for sizes of about 5 microns. I thus estimate that they are accurate to at least 1e-3. From a few plate solves of my own images, I estimate the error on the plate scale to be of that order also. The 1% extra length found should thus be significant. No big deal, but is this just my copy?
To test this, I used AB to compute focal lengths from a bunch of images taken with ESPRIT 100EDs. With AB's API, I got plate scales for 1220 images taken during the past year, with a variety of cameras: Monos, OSCs & DSLRs. I took the median value for each user (assuming a single copy each), and computed the histogram. This gives the step curve in the graph below:
It is peaked at 555 mm (meaning that my copy is pretty typical), with a dispersion of a few mm. One can check that there is no significant dependence of the focal length with pixel sizes, meaning that uncertainties on these latter are not the source of the dispersion. The pastel-colored curves are histograms for individual users with more than 20 images, which gives an idea of the measurement dispersion for individual copies. There are a few stray values (and several possible causes) but they should not affect the conclusions.
I don't know why the focal length is listed as 550 mm and not 555. One answer could be: "who cares?". Another could be that the focal length of the triplet is indeed 550 and that the field corrector used by all imagers increases the effective length a bit. Or something else.
Anyway, I did this for fun and out of curiosity, and the 1% difference from the nominal has absolutely no importance. But who knows, maybe somebody will care, hence this long post
CS,
Frédéric
PS: AB is really a fantastic resource!
Love this take on it.
That was a pure geeky procrastination activity 
