The out of focus blur figure of a point source

Doug Kerr · Jun 16, 2014

On the table is the following question:

Does the basic (geometric) equation for the diameter of the blur figure created from an out-of-focus point object give a useful approximation of that diameter for a substantial out-of-focus situation for real lenses?

We recognize that for an actual lens, many matters (including various aberrations) will result in a luminance profile across the blur figure that is not the "classical" one (uniform luminance across a disk with a sharp boundary). Thus, the concept of the boundary must often be taken in a creative way.

And we recognize that, if the aperture stop is substantially non-circular in outline, the nominal boundary of the blur figure may be substantially non-circular, so of course the concept of "diameter" must be taken in a creative way. (The very same is in fact true with regard to the f-number of a lens: a lens with a substantially-non-circular entrance pupil does not really have an f-number!)

But despite all that, does the result of the basic equation nevertheless typically give a useful approximation of the "diameter" of the blur figure in a substantially out-of-focus case?

For example, in this image:

William Brawley: Christmas Bokeh. Courtesy Wikimedia Commons

If the sizes of the subject lights (as projected on this image) were very small compared to the sizes of the blur figures (so that the "point source" conceit is reasonably applicable), then if we make some reasonable interpretation of what a circular boundary is for each of the blur figures, are their diameters "reasonably consistent" with what is predicted by the basic blur figure equation?

I have (perhaps inappropriately) always thought that to be true. But I may be gravely in error.

Does anyone have any information that would enlighten me on the realities here?

Thanks.

Best regards,

Doug

Jerome Marot · Jun 16, 2014

All you need is love.

The image is from this site. Slightly better explanations here.

Doug Kerr · Jun 16, 2014

Hi, Jerome,

Jerome Marot said:
All you need is love.

That is all wondrous. Thanks so much.

Best regards,

Doug

Doug Kerr · Jun 16, 2014

It is interesting that in the much-reviled "classical" (geometric) equation for the diameter of the blur spot from an out-of-focus point object, that diameter is given by:

Dk

where D is the diameter of the entrance pupil (that of course assumes a nominally-circular entrance pupil) and k is a complicated function of focal length, focus distance, and object distance (see below).

That being the case, it is easy to think that the "theoretical" blur figure might be the image of the entrance pupil at a magnification k.

So if we provide, in front of the lens, an aperture stop that is wholly within the actual entrance pupil, it becomes the new entrance pupil. If it is "heart-shaped", we might expect the blur figure to be "heart-shaped." (Aww!)

And, recognizing that aberrations (and diffraction) will give the blur figure a boundary that is not as abrupt as the boundary of our external aperture stop, so that we must be a little creative in deciding what the boundary of the blur figure is, and thus its "size", I very strongly suspect that the "size" of the blur figure is k times the size of the exterior aperture stop figure.

But maybe not. Again, I await a demonstration of this.

By the way, the expression for k is:

k = abs(1-(P(S-f))/(S(P-f)))

where P is the distance at which the camera is focused, S is the distance to the point object, and f is the focal length of the lens, all in consistent units (perhaps mm).

Note that if P=S (a point object at the focus distance: proper focus), k becomes zero (that is, a point image would be formed, of course in the absence of aberrations and diffraction).

Best regards,

Doug

Doug Kerr · Jun 17, 2014

Some authors have intimated that the equations for the diameter of the blur figure from an out-of-focus point object are only reliable for a thin lens. That is not so. The optical theory behind these is equally applicable to a non-thin lens (of course assuming that, as always, we measure distances from the right places!).

But in fact the equations are only precisely applicable if the lens is free from certain aberrations (most importantly spherical aberration).

In fact, it has been suggested that, owing to this latter issue, the equations are essentially useless for use in a "greatly out of focus" regime with typical lenses of interest to us.

Of course, our usual concerns with the diameter of the blur circle are such that a precise result is not needed (nor in some cases even possible). Thus, if the usefulness of the equations is generally doomed by the potential impact of spherical aberration, that potential impact would have to be substantial.

Of course, those with the proper knowledge, data, and computational tools should be readily able to broadly estimate the potential error in this regard for typical lenses, but I do not have any of that.

But to get some insight into this, I decided to measure the "diameter" of the blur figure created from a "greatly out-of-focus" point object with a camera and lens I had handy.

The test was done with a Canon EOS 40D body and a Canon EF 70-200mm f/4L IS USM lens. The test object was a star (Alpha Orionis - Betelgeuse in Orion).

The first test was as follows:

Focal length (per scale): 200 mm
Aperture: f/4.0
Focus distance (per scale): 5 m (this is not highly precise)
Object distance: essentially infinite (about 640 light-years)

I bracketed exposure time and ISO sensitivity until I got an exposure result in which the brightest part of the blur figure was just a bit below saturation.

The star was located very nearly on the optical axis.

We see the result here:

The image overall is 500 px × 500 px.

There are probably rings in the blur figure I cannot discern, but then they should have no significant effect on the visual result in a "rich background" setting.

The red circle shows the calculated blur figure diameter (2.083 mm, 225 px) for the parameters of the test.

The fact that the figure is not quite circular is worrisome. It may reflect some decentering in the lens.

Best regards,

Doug

Jerome Marot · Jun 17, 2014

You are using a very well corrected lens as an example. You would get very different results with a fast wide angle lens. You may also want to try the same test further away from the optical axis. This is more representative of a "bokeh" situation where the defocussed parts of the picture are rarely spot on centre.

fahim mohammed · Jun 17, 2014

For me, it is the print of an image that matters. Is it visually pleasing to me. Are the oof areas appropriate for the situation I am trying to depict.

I am not a lens designer. I choose to buy lenses after seeing what they can do, in my real life photography.

I find lens design academics tedious. And of no value in my use of the lens/lenses.

The cost of the lens, for me, has paid for the nerds designing the lens. It's value, it's only value, is whether the lens justifies it's cost to me and the images the lens helps me to make.

Asher Kelman · Jun 17, 2014

fahim mohammed said:
..........

The cost of the lens, for me, has paid for the nerds designing the lens. It's value, it's only value, is whether the lens justifies it's cost to me and the images the lens helps me to make.

Fahim,

Without "nerds" obsessed with the technical challenges of improving imaging systems, there'd be no digital editing that we take for granted, LOL! Cameras, BTW, devalue with time, except perhaps a few rare classics. however the best lenses hold their value and might even be great investments.

In the case of Canon's "big whites", the new lenses are so astronomically high that they protect older models from getting devalued. Although bulkier than diamonds, great lenses are a reasonably safe investment.

...and I'm grateful for guys like Doug, who make all this possible so we can just choose the lens we like and raid the entire planet for images.

Asher

Doug Kerr · Jun 17, 2014

Erratum

I am greatly embarrassed to discover a computational error and an editorial error in my report above.

The corrected result is quite different in its implications than the original one.

I repeat the report in its entirety, corrected. The figure is different, and changes in the data and text are in blue.

My apologies for the error.

************

Some authors have intimated that the equations for the diameter of the blur figure from an out-of-focus point object are only reliable for a thin lens. That is not so. The optical theory behind these is equally applicable to a non-thin lens (of course assuming that, as always, we measure distances from the right places!).

But in fact the equations are only precisely applicable if the lens is free from certain aberrations (most importantly spherical aberration).

In fact, it has been suggested that, owing to this latter issue, the equations are essentially useless for use in a "greatly out of focus" regime with typical lenses of interest to us.

Of course, our usual concerns with the diameter of the blur circle are such that a precise result is not needed (nor in some cases even possible). Thus, if the usefulness of the equations is generally doomed by the potential impact of spherical aberration, that potential impact would have to be substantial.

Of course, those with the proper knowledge, data, and computational tools should be readily able to broadly estimate the potential error in this regard for typical lenses, but I do not have any of that.

But to get some insight into this, I decided to measure the "diameter" of the blur figure created from a "greatly out-of-focus" point object with a camera and lens I had handy.

The test was done with a Canon EOS 40D body and a Canon EF 70-200mm f/4L IS USM lens. The test object was a star (Alpha Orionis - Betelgeuse in Orion).

The first test was as follows:

Focal length (per scale): 200 mm
Aperture: f/4.0
Focus distance (per scale): 10 m (this is not highly precise)
Object distance: essentially infinite (about 640 light-years)

I bracketed exposure time and ISO sensitivity until I got an exposure result in which the brightest part of the blur figure was just a bit below saturation.

The star was located very nearly on the optical axis.

We see the result here:

The image overall is 500 px × 500 px.

There are probably rings in the blur figure I cannot discern, but then they should have no significant effect on the visual result in a "rich background" setting.

The red circle shows the calculated blur figure diameter (1.024 mm, 177 px) for the parameters of the test.

The fact that the figure is not quite circular is worrisome. It may reflect some decentering in the lens.

This shows that the "diameter" of the blur figure is indeed substantially greater than that suggested by the ideal "geometric" calculation, by a factor of about 1.35. We may conjecture that this is in great part (perhaps wholly) due to the effect of spherical aberration.

Thanks to Jerome for alerting me to this matter.

Best regards,

Doug

Doug Kerr · Jun 17, 2014

Hi, Fahim,

fahim mohammed said:
I find lens design academics tedious.

Me too.

I was worn the hell out when i went to bed last night.

As you can see from my erratum, I was apparently in no condition for such tedium at the time.

Best regards,

Doug

Bart_van_der_Wolf · Jun 17, 2014

Doug Kerr said:
The fact that the figure is not quite circular is worrisome. It may reflect some decentering in the lens.

Hi Doug,

I wouldn't worry, it's more likely due to the earth's rotation and/or atmospheric turbulence during the exposure time. In fact I'm amazed it is not elongated more, unless you were using an azimuthal mounting device.

Cheers,
Bart

fahim mohammed · Jun 17, 2014

I, too, am grateful to those that are obsessed with technical challenges of improving not only imaging systems but improvements in all fields of science.

But that is missing my point.

Fahim, said Faisal, are you ready? Yes, I said. That is the latest GE equipment. There is the Siemens, and Philips respiratory systems. The lights above are..and he started going into the details of how lights should be in the OR. Being a ' nerd' himself, he said you see the heart lung machine functions like this..I remember I said, spare me the bother Faisal, just get on with it...I felt I was going into a slumber. Things were hazy..a Scandinavian voice in the distant was faint..' yes his respiration is good...2 seconds..I woke up later with my family around me. I am sure the machines must have performed with precision. As did the people using the tools.

We import from the States, Japan, Germany, said the bank's customer to me. I want to shield myself from the foreign currency price fluctuations, he said. Being a ' nerd ', I explained all about options, forwards, saddles, reverse hedges etc. He went to my MD. I want to get my costs protected and your guy ( me!! ) goes on and on about things I do not understand. Can your bank do this for me or not.

I was called in. Of course, I said. This is the percentage cost to you, I told the customer. That's all I need to know, he said. Why are you trying to impress me with the tech details I do not understand, he added. I am sure your costing has your bonus built in.

I am grateful to Ibn Haitham too, for his theories on light.

Asher Kelman said:
Fahim,

Without "nerds" obsessed with the technical challenges of improving imaging systems, there'd be no digital editing that we take for granted, LOL! Cameras, BTW, devalue with time, except perhaps a few rare classics. however the best lenses hold their value and might even be great investments.

In the case of Canon's "big whites", the new lenses are so astronomically high that they protect older models from getting devalued. Although bulkier than diamonds, great lenses are a reasonably safe investment.

...and I'm grateful for guys like Doug, who make all this possible so we can just choose the lens we like and raid the entire planet for images.

Asher

Doug Kerr · Jun 17, 2014

Hi, Bart,

Bart_van_der_Wolf said:
Hi Doug,

I wouldn't worry, it's more likely due to the earth's rotation and/or atmospheric turbulence during the exposure time. In fact I'm amazed it is not elongated more, unless you were using an azimuthal mounting device.

Well, of course! I finally ended up with a 15 s exposure time!

Thanks.

Best regards,

Doug

fahim mohammed · Jun 17, 2014

They gave me a machine. They said it shall help me. I just put the mask on, switch on the machine and gently go to sleep.

It has helped me a lot. It is made by Philips.

I am sure it has latest technology in it. It records data too. What and how? I am grateful to the ' nerds ' at Philips.

Doug Kerr · Jun 17, 2014

Hi, Jerome,

Jerome Marot said:
You are using a very well corrected lens as an example. You would get very different results with a fast wide angle lens.

No doubt.

A problem with testing such is that at 28 mm (f/2.8), for example, with the 10 m to infinity setup, on my camera, the theoretical diameter of the point object blur figure is only about 5 px.

Thanks.

Best regards,

Doug

Bart_van_der_Wolf · Jun 17, 2014

Doug Kerr said:
This shows that the "diameter" of the blur figure is indeed substantially greater than that suggested by the ideal "geometric" calculation, by a factor of about 1.35. We may conjecture that this is in great part (perhaps wholly) due to the effect of spherical aberration.

Hi Doug,

That seems like a lot of difference to me to explain from spherical aberration alone. Actually, when looking at the EXIF data, the lens is reporting a focus distance of 6.95 - 8.19 m, which would explain a lot of the observed blur diameter.

Infinitely distant objects, when focusing at 10 m (= image magnification of 1:49) have a blur size of:
M * f / N , or
1/49 * 200 / 4 = 1.0204 mm, divided by the EOS-40D's sensel pitch of 0.00571mm = 178.7 pixels, which closely corresponds to what you calculated.

At 6.95 m that would change to 1.48mm or 259.5 pixels, and at 8.19 m it would change to 1.25mm or 219.2 pixels. So it seems that either the distance scale on the lens is not all that accurate, or that the lens reports very different distance information. I have a feeling that the lens electronics are 'slightly' more accurate in this case.

Maybe trying to calibrate that EXIF distance setting to an actual object at that distance from the entrance pupil, would allow to get a closer approximation of the additional effect of Spherical Aberration. It will also reveal how useful those distance data fields in the EXIF are, or whether it's more something for internal use (DOF calculation capability of some camera models, and other uses like lens calibration feedback).

Cheers,
Bart

Doug Kerr · Jun 17, 2014

Hi, Bart,

Bart_van_der_Wolf said:
That seems like a lot of difference to me to explain from spherical aberration alone. Actually, when looking at the EXIF data, the lens is reporting a focus distance of 6.95 - 8.19 m, which would explain a lot of the observed blur diameter.

I had meant to look into that (having not much confidence in the focusing scale, which is rather "compressed" in that regime anyhow) but ran out of energy! My overall preparations for the test were rather agricultural! (I was in my pajamas, but I did put on shoes!)

Infinitely distant objects, when focusing at 10 m (= image magnification of 1:49) have a blur size of:
M * f / N , or
1/49 * 200 / 4 = 1.0204 mm, divided by the EOS-40D's sensel pitch of 0.00571mm = 178.7 pixels, which closely corresponds to what you calculated.

At 6.95 m that would change to 1.48mm or 259.5 pixels, and at 8.19 m it would change to 1.25mm or 219.2 pixels. So it seems that either the distance scale on the lens is not all that accurate, or that the lens reports very different distance information. I have a feeling that the lens electronics are 'slightly' more accurate in this case.

Yes, I would suspect you are right.

The diameter of the blur figure seems to be about 241 px.

Maybe trying to calibrate that EXIF distance setting to an actual object at that distance from the entrance pupil, would allow to get a closer approximation of the additional effect of Spherical Aberration. It will also reveal how useful those distance data fields in the EXIF are, or whether it's more something for internal use (DOF calculation capability of some camera models, and other uses like lens calibration feedback).

Yes, that would be worthwhile. I had contemplated doing just that, but was too lazy!

I may set up an illuminated "short-distance" target for that purpose and run the test using that to set the focus distance.

Thanks so much for your help with this.

Best regards,

Doug

Doug Kerr · Jun 17, 2014

Bart has called to mind that the Exif data in the image I worked from, as interpreted by "Jeffrey's Exif viewer", suggests a focus distance in the range of 6.95 m to 8.19 m.

I had set the lens by focusing scale to a focus distance of 10 m, but the focusing scale is quite compressed in that regime (and there are no actual scale marks), so I have little confidence in that.

If, just for kicks, we take the midpoint of the Exif-reported range as the actual focus distance, the diameter of the blur figure as reckoned using the classical geometric formula would be 238 px.

Just for kicks, I plotted a red circle of that diameter on the blur figure image:

Note that, as Bart reminded me, the elongation of the blur figure along a diagonal axis is no doubt primarily due to motion blur during the 15 s exposure I used.

Best regards,

Doug

Jerome Marot · Jun 17, 2014

I can't wait for the next episode in this saga.

Doug Kerr · Jun 17, 2014

Hi, Jerome,

Jerome Marot said:
I can't wait for the next episode in this saga.

You will have to.

Best regards,

Doug

Jerome Marot · Jun 17, 2014

Doug Kerr said:
You will have to.

I'll survive. Take care, Doug.

Doug Kerr · Jun 17, 2014

Bart had pointed out that while my test was done with the focus distance set to "10 m" on the focusing scale (which is of course not inherently very precise, and who knows how accurate it is), the Exif metadata for my test image showed a focus distance as reported by Jeffrey's Exif viewer (JEV) of in the range 6.95 m to 8.19 m.

I decided to look a little into this.

Of course, the camera reports the focus distance (which it presumably gets from the lens) as one of a number of discrete values. I suspect that the discrete values in the neighborhood of 10 m are:

6.95 (m)
8.19
9.62
11.40
14.23

I don't know whether both values reported by JEV actually comes from the Exif metadata. I think it is very possible that the "upper" value is the one actually reported in the Exif metadata, and JEV is kind enough to enlarge the story by reporting the next lower value from a table in the viewer.

I do note that most applications that do report this metadata item report only the upper one shown by JEV.

I did a very limited test with my Canon EOS 40D body and my Canon EF 70-200mm f/4L IS USM lens.

I manually focused the camera (using Live View at 10x magnification) at a target at measured distances (to the focal plane) of 9.85 m, 10.00 m, and 10.15 m. At each focus setting, I fired a test shot, and examined the metadata with JEV. The results were as follows:

Focus__________Reported focus
distance (m)____distance range (m)

_9.85 ___________ 9.62 - 11.4
10.00 ___________ 9.62 - 11.4
10.15 ___________ 11.4 - 14.23

This means that the break between the range that is considered 9.62 - 11.4 and the range that is considered 11.4 - 14.23 (that point would actually be 11.4) occurs in my system at a focus distance slightly over 10.00 m (let's assume 10.1).

If we consider the "upper" value to be the "reported value", then the break between reporting 11.4 and 14.23 in my system occurs at about 10.1 m.

Possible intent A

If the intent is to round the actual value to the nearest established discrete value and report that, then the ideal setup would be this:

In terms of a reported value that would be the upper value as reported by JEV, the break between reporting 9.62 and reporting 11.4 would occur at about 10.5. The break between reporting 11.4 and reporting 14.23 would occur at about 12.8.

Thus a report of 11.4 would (ideally) mean that the actual value was in the range 10.5 - 12.8 (not 9.62 - 11.4, as intimated by the presentation in the JEV).

Add to this the fact that in the summary at the head of the JEV report, for that situation, it says that the depth of field is 11.4-9.62.

In any case, if what I just described is the intent (and who knows what evil lurks in the Mind of Canon), then (in this area) the report in my system is about 2.7 m too large.

Possible intent B

If in fact the intent is that an (upper) report of 11.4 means an actual value in the range 9.62 - 11.4 (as intimated by the language in JEV), then the break between reporting 9.62 - 11.4 and reporting 11.4 - 14.23 should come at 11.4.

In that case, for my system, in this area, the report is about 1.3 m too large.

Best regards,

Doug

Doug Kerr · Jun 18, 2014

Indeed FocusDistanceUpper and FocusDistanceLower are distinct items in the Maker Note portion of the Canon EOS 40D Exif metadata.

I note that in the Canon Powershot cameras (including the G series) FocusDistanceLower seems to be always zero (I have seen this mentioned in some forums).

Best regards,

Doug

Don Ferguson Jr. · Jun 18, 2014

Asher Kelman said:
Fahim,

...and I'm grateful for guys like Doug, who make all this possible so we can just choose the lens we like and raid the entire planet for images.

Asher

Never knew Doug was a lens engineer for Canon or Nikon.

Don

Doug Kerr · Jun 18, 2014

I had made preparations so that last evening I could do "blur circle of a misfocused star" tests with the lens set to a known focus distance (by manually focusing on a focus target at that distance).

But, by the time it was dark, there was substantial cloud cover such that the test would not have been practical (rather infrequent here in Alamogordo).

I have taken this as a sign.

Best regards,

Doug

Doug Kerr · Jun 19, 2014

The "sign" notwithstanding, last night I repeated my basic test of spot size with a distant star as the object, this time with better knowledge of the focus distance of the camera, and using a shorter exposure to reduce the effects of motion blur due to the rotation of the earth. A shot was also taken with the object near the corner of the frame.

Again, the camera comprised a Canon 40D body with a Canon EF 70-200mm F4L IS USM lens.

As before, the test object was Alpha Orionis (Betelgeuse in Orion) (current magnitude about 0.42). Its subtended diameter from Earth is about 0.045 arc seconds. For the focal length I used, the actual theoretical diameter of the star's image on the focal plane would be about 8.7 µm, or about 1.5 sensel pitch.

The parameters of the shots were:

Focus distance (from focal plane): 10.0 m (by test target)
Object distance: essentially infinite
Focal length: 200 mm
Sensitivity: ISO 3200 nominal
Exposure time: 4 sec
Aperture: f/4.0

The first shot was with the object very nearly centered in the frame. Here we see a 300 px × 300 px crop at original camera resolution:

There was slight atmospheric haze (not-yet-gone clouds), which probably results in the somewhat vague boundary of the figure; I do not think that is of any consequence to the matter of interest.

The red circle shows the theoretical spot diameter based on an assumed focus distance (as required by the equation, to the first principal point, whose location had to be estimated) of 9.85 m. That diameter is 1.036 mm (179 px).

The second shot was with the same parameters but with the object located some distance from the center of the frame, as seen in this reduced-resolution image:

The center of the object was about 3.24° off-axis.

Here we see a 300 px × 300 px crop at original camera resolution:

Again, the red circle shows the theoretical spot diameter on the same premises as before.

The shape of the figure is no doubt a reflection of the actual entrance pupil, which in this off-axis case is presumably "clipped" from the one created by the aperture stop by the boundary of the lens' first element.

******

With respect to the reporting of focus distance in the Exif metadata, for both shots this was reported as the range 9.62-11.4 m.

************

The presentation of these results is in no way meant to denigrate the warning that, in general, we need to be cautious in using a calculated spot diameter for blur planning since spherical aberration and coma (its more general case) may well enlarge the actual spot diameter from its theoretical size.

Best regards,

Doug

Bart_van_der_Wolf · Jun 19, 2014

Hi Doug,

This has turned out to be an interesting study. We learned something about pitfalls we may encounter, about distance recorded in EXIF (which BTW might be related to controlling flash output on some models), and that (for this) lens theory and practice may align pretty well with regards to blur circle diameter. Of course, the brightness distribution and actual size be imaged a bit different from case to case, depending on the actual lens corrections.

The lens you used, in my experience, performs quite well at f/4 (its widest aperture), although I often use it at f/4.5 or f/5.0 because it becomes a bit sharper in the focal plane, and the built-in Image Stabilization still functions well enough to allow hand held operation despite the resulting slightly longer exposure times.

The test object itself also has an interesting history, for those who might wonder.

Thanks for sharing the experiment, and results.

Cheers,
Bart

Asher Kelman · Jun 19, 2014

Doug Kerr said:
......

As before, the test object was Alpha Orionis (Betelgeuse in Orion) (current magnitude about 0.42). Its subtended diameter from Earth is about 0.045 arc seconds. For the focal length I used, the actual theoretical diameter of the star's image on the focal plane would be about 8.7 µm, or about 1.5 sensel pitch.

The parameters of the shots were:

Focus distance (from focal plane): 10.0 m (by test target)
Object distance: essentially infinite
Focal length: 200 mm
Sensitivity: ISO 3200 nominal
Exposure time: 4 sec
Aperture: f/4.0

The first shot was with the object very nearly centered in the frame. Here we see a 300 px × 300 px crop at original camera resolution:

There was slight atmospheric haze (not-yet-gone clouds), which probably results in the somewhat vague boundary of the figure; I do not think that is of any consequence to the matter of interest.

The red circle shows the theoretical spot diameter based on an assumed focus distance (as required by the equation, to the first principal point, whose location had to be estimated) of 9.85 m. That diameter is 1.036 mm (179 px).

The second shot was with the same parameters but with the object located some distance from the center of the frame, as seen in this reduced-resolution image:

The center of the object was about 3.24° off-axis.

Here we see a 300 px × 300 px crop at original camera resolution:

Again, the red circle shows the theoretical spot diameter on the same premises as before.

The shape of the figure is no doubt a reflection of the actual entrance pupil, which in this off-axis case is presumably "clipped" from the one created by the aperture stop by the boundary of the lens' first element.

******

With respect to the reporting of focus distance in the Exif metadata, for both shots this was reported as the range 9.62-11.4 m.

************

The presentation of these results is in no way meant to denigrate the warning that, in general, we need to be cautious in using a calculated spot diameter for blur planning since spherical aberration and coma (its more general case) may well enlarge the actual spot diameter from its theoretical size.

Best regards,

Doug

Brilliant!

Bravo, the universe does know you're right!

Asher

Doug Kerr · Jun 19, 2014

Hi, Asher,

Asher Kelman said:
Brilliant!

Thank you.

Best regards,

Doug

Doug Kerr · Jun 19, 2014

Today we were on the indoor test range, this time testing with the EOS 40D and the EF-S 18-200 f/3.5-5.6 IS.

The object today was a pinhole on an LED flashlight, not of infinitesimal size, and was far closer than Alpha Orionis. There were in fact many compromises in this test series, but there are still some interesting results.

The test were done at an (indicated) focal length of 18 mm. The object was at a distance of about 7.2 m. The near focus distance was at about 1 m, but uncertainty about where the first principal point of the lens is makes that subject to some uncertainty (and of course with an f/3.5 aperture and a focal length of 18 mm, manual focus is not too "snappy" anyway").

In the first shot, focus was on the object so we could see the size of its image, hopefully free of any misfocus blur. The object was nominally centered in the frame. Here we see a 40 px × 40 px crop of the test shot, at 5x camera resolution:

The yellow circle has diameter 20 px, and is provided for ease in visualizing the scale of the figures.

I would characterize the diameter of this figure as about 11 px (although my choice as to the "boundary" is very arbitrary).

Next the camera was focused at (hopefully) 1 m and the shot taken again (the object again being nominally centered in the frame). Here we see the result (the circumstances of presentation being the same as for the earlier image):

Again the yellow circle has diameter 20 px. I would characterize the diameter of this figure as about 14 px (trying to use a comparable visual criterion as to the "boundary"). Since that is not greatly larger than the diameter of the spot for the object in focus, it is difficult to deduce what the spot size would have been for an "infinitesimal" object. (Yes, I could have used a smaller pinhole, but I didn't.)

On the right, we have the same figure, but I have shown (as the red circle) the calculated spot diameter, which is approximately 14 mm. (But this is not highly reliable, owing to the uncertainty as to the actual focus distance.)

In the third shot, the object was substantially off-center. (See next message for the "little map" of that - it was "over quota" here). Same drill as before:

I would characterize the diameter of this figure as about 15 px (trying to use a comparable visual criterion as to the "boundary"). We can certainly see that the figure is not as nearly "circular" as before, and we can perceive some chromatic asymmetry. Likely we are seeing some impact of coma here, but not so much as to disrupt the matter of spot size.

On the right, we have the same figure, with the red circle showing the calculated spot diameter, approximately 14 mm.

Very interesting.

Best regards,

Doug

The out of focus blur figure of a point source

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