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up vote 2 down vote favorite

How do I calculate the object size when I have

  • focal length = 25mm
  • distance to object = 700mm
  • CCDs pixel size = 4,4µm ?

My camera is this one. Appreciated!

Edit: Could this work:

real height = (object px height * pixel size * distance)/(focal length) ?

share|improve this question
What is the width of the sensor in mm? – ElendilTheTall May 23 '12 at 10:42
I actually don't know for sure, but I found on this website "in the case of the 1/1.8" tube the image area was 7.176mm x 5.329mm" – Wilhelmsen May 23 '12 at 10:44
1  
This is quite similar to another question which I answered. – Håkon K. Olafsen May 23 '12 at 11:33

3 Answers

up vote 3 down vote accepted

There are several problems with your solution - one problem with your math and lots of real world problems that will seriously impact the accuracy of your calculation.

The problem with your formula is that you didn't consider the gaps between pixels - something that is 10 pixels wide in the image actually covers 10 pixels + 9 gaps on the sensor - by ignoring the gaps your calculation will always return a smaller size than the object true size by a constant factor.

As for the real world problems - the first is that this will only work if the object you are measuring is exactly parallel to the camera sensor (or you'll have perspective distortion).

The second is that focal lengths are not accurate, the number in the spec is rounded to the nearest common focal length and even that only when the lens is focused to infinity (focal length changes with focus).

And that's even before we consider distortion caused by the lens and other imperfections of real world optical devices.

Most of the problems can be solved by taking a test shot of an object with a known size

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Thank you, very descriptive! The problem is that my teacher is a dick, and won't accept these facts, telling us only to ignore such data as you describe. Thank you tho, will mention it! – Wilhelmsen May 23 '12 at 14:14
up vote 1 down vote

Quick mental examination says your formula looks correct.

Almost intuitively:

  • Image_height x (Distance/Focal_length) = Real height

    so

  • (Pixel_pitch x pixels) x (Distance/Focal_length) = Real Height

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up vote 0 down vote

To determine the size of an object in image you need to know the field of view. There are numerous calculators online, like this one.

According to this Wikipedia article the crop factor of a 1/1.8" sensor is 4.84. Putting that information, along with the focal length and subject distance information you've supplied, into the FoV calculator gives field of view measurements of:

Width - 208.26mm

Height - 138.84mm

You can now measure the object on the photo and calculate the physical size by calculating the percentage of the image it fills, e.g. if the object takes up 50% of the width of the image, it is 104.13mm wide in 'real life'.

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2  
Beware that you can't trust specifications here, at least if you want more than ballpark accuracy. The actual size of any given 1/1.8"-class sensor may vary, and lens focal length is often rounded or just plain given with poor accuracy and precision. – mattdm May 23 '12 at 11:37
I am not supposed to use online calculators for this, since I need to be able to calculate using only these sizes by hand. – Wilhelmsen May 23 '12 at 11:38
@Wilhelmsen The site gives you all the formulas for calculating by hand. – ElendilTheTall May 23 '12 at 11:46

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