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08-31-2012, 02:58 AM   #1
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How to calculate size of object on the sensor?

Hello!

Perhaps, my question is too theoretic. May be, it does not refer to the beginners section. Nevertheless, I put it here as I am a beginner.
I would like to know how to evaluate the objectís size on the cameraís sensor roughly. As I understand, the objectís size on the sensor depends from the objectís original size, the distance between the camera and the object and the focal length.
When I asked question how to determine minimum shutter speed for moving objects in this forum (https://www.pentaxforums.com/forums/pentax-beginners-corner-q/165146-how-calc...g-objects.html), I received very good answers and links to interesting web-pages. According to one page, the objectís size on the sensor is reduced by the factor R = F/D, where F is the focal length and D is the distance between the camera and the object. I rearranged the formula, did some simplifications and formulated such a formula:

Objects size on sensor (in mm) = Objects original size (in m) * focal length (in mm) / distance between camera and object (in m)

I tried to carry out such a calculation for the high building or tree:
- the objects is 20 m tall (high),
- the distance between the camera and the object is 25 m,
- the focal length is 28 mm (widest angle for my standard kit lens).

So the calculation is the following: 20 * 28 / 25 = 22,4 mm

I have Pentax K-x which has APS-C (23.6 x 15.8 mm) sensor. If the calculation is correct, the objects size on the sensor exceed the sensorís length (15.8 mm) but it is under the width of the sensor (23.6 mm). So I could take the picture by holding camera vertically. And the objectís size will take 95% of the width of the sensor and the photograph, in turn.

In these calculations I have not taken into account the crop factor. As I understand, it does not affect the objectís size on the sensor. It only determines whether the objectís size exceeds the dimensions of the sensor or not.

I would like to know whether this formula is correct for rough calculations. Such calculations could help to determine which lenses (for example, 18-55 or 50-200) take before going out to do shooting .

Best regards
Alberts

08-31-2012, 03:10 AM   #2
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Your calculation is right. That provided that you shoot objects "far" away, since your calculations implicitly takes field of view into account. Note that FOV taken into account is FOV at infinity (i.e. very far away objects). However this formula is good enough for almost everything beyond macro shooting.

In macro world some other stuff comes into play, such as focus system (internal, front and/or back movement of lenses during focus), but that is completely different issue, depending much on lens design.
08-31-2012, 04:22 AM   #3
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You need to be really careful with units.

You can't match randomly mm and meters and get a correct answer. You were very lucky

The formula, is as folows

Image size = subject size x focal length / subject distance. Keep all units in either meters or mm.

This formula holds true for subject distance >> focal length (a good rule is at least 10x)

Note ass well this only holds true for primes, and zooms that do not change focal length when focusing closer than infinity. Some sup zooms like 18-200mm lenses with wide zoom ranges only hold correct focal lengths at infinity focus, and reduce the focal length as part of the focusing, as you focus in to shorter distances, some super zooms reduce focal length by as much as 30% compared to reported focal length, it's just the nature of the beast
08-31-2012, 04:32 AM   #4
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QuoteOriginally posted by Lowell Goudge Quote
You need to be really careful with units.

You can't match randomly mm and meters and get a correct answer. You were very lucky

The formula, is as folows

Image size = subject size x focal length / subject distance. Keep all units in either meters or mm.

This formula holds true for subject distance >> focal length (a good rule is at least 10x)

Note ass well this only holds true for primes, and zooms that do not change focal length when focusing closer than infinity. Some sup zooms like 18-200mm lenses with wide zoom ranges only hold correct focal lengths at infinity focus, and reduce the focal length as part of the focusing, as you focus in to shorter distances, some super zooms reduce focal length by as much as 30% compared to reported focal length, it's just the nature of the beast

I took into account units of measure . As the objectís original size and the distance between the camera and the object are expressed in meters, the ratio is without unit (meters are divided by meters). So when the focal length is multiplied by the ratio, the outcome (the objectís size on the sensor) has the same unit of measure as the focal length.

08-31-2012, 04:35 AM   #5
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Why need to mess with focal length and distance, what's wrong with the plain old rule of three? (measure the size of the object in pixels, compare it to the size of the total image in pixels which you know, then transpose everything in millimeters)
08-31-2012, 04:57 AM   #6
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QuoteOriginally posted by kcobain1992 Quote
Why need to mess with focal length and distance, what's wrong with the plain old rule of three? (measure the size of the object in pixels, compare it to the size of the total image in pixels which you know, then transpose everything in millimeters)
Hello!

My goal was to find out a way how to calculate (estimate) the size of the subject on the sensor before going to do shooting. If I roughly know the subjectís size in real life and the distance between the subject and the camera, I can approximately estimate whether the lens with given focal length (or range of focal length) will allow me to catch the whole subject on the sensor. If the subjectís size on sensor is too small, I can consider using lenses with larger focal length. For such purposes I tried to figure out the formula.
I should recognise that I have not heard of the plain old rule of three you mentioned. Could you tell me more about it?

Best regards,
Alberts
08-31-2012, 05:03 AM   #7
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QuoteOriginally posted by kcobain1992 Quote
Why need to mess with focal length and distance, what's wrong with the plain old rule of three? (measure the size of the object in pixels, compare it to the size of the total image in pixels which you know, then transpose everything in millimeters)
If you look at Alberts desire, to estimate the image size he will get, in advance of shooting, knowing his shooting distance and subject, you need to do a calculation.

Simply measuring the image size after the fact in pixels does nothing to help him plan
08-31-2012, 05:04 AM   #8
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QuoteOriginally posted by Alberts Quote
I took into account units of measure . As the objectís original size and the distance between the camera and the object are expressed in meters, the ratio is without unit (meters are divided by meters). So when the focal length is multiplied by the ratio, the outcome (the objectís size on the sensor) has the same unit of measure as the focal length.
It's not clear from your formula you were considering units at all, you got lucky, normally when doing a calculator you do not change units between the different data entries. You keep all units the same.

08-31-2012, 05:05 AM   #9
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QuoteOriginally posted by Alberts Quote
I should recognise that I have not heard of the plain old rule of three you mentioned. Could you tell me more about it?
Cross-multiplication - Wikipedia, the free encyclopedia
Anyway, I misunderstood your intentions.
08-31-2012, 05:21 AM   #10
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QuoteOriginally posted by Lowell Goudge Quote
It's not clear from your formula you were considering units at all, you got lucky, normally when doing a calculator you do not change units between the different data entries. You keep all units the same.
Actually, I expressed all the variables in meters when I started formulating the formula. Then I noticed that I should the result divide by 1000 in order to covert the result into mm. At the same time, I was multiplying the focal length with 1000 to convert it into m. By doing some mathematical simplifications and rearrangements, I expressed result in mm and focal length in mm.

Objects size on sensor (in m) = Objects original size (in m) * focal length (in mm)* 1000 / distance between camera and object (in m)

Objects size on sensor (in mm) = Objects size on sensor (in m)/1000

So:

Objects size on sensor (in mm) = (Objects original size (in m) * focal length (in mm)* 1000 / distance between camera and object (in m)) / 1000

The final result:

Objects size on sensor (in mm) = Objects original size (in m) * focal length (in mm) / distance between camera and object (in m)
08-31-2012, 05:23 AM   #11
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QuoteOriginally posted by kcobain1992 Quote
Cross-multiplication - Wikipedia, the free encyclopedia
Anyway, I misunderstood your intentions.
Thanks for the link. Now I understand the issue . In my language this rule is called in different way (the approximate translation might be ďthe rule of crossĒ). So I cannot recognise what the rule of three means.
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