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3. Distortion
As stated in paragraph 1.2, scale (image size) depends on distances of object and image.
Scale thus defines the size of the entire image.

Going into details of the image you will notice a slightly varying "micro-scale".

For example, details at the rim of the image might be reproduced at a larger scale; details in the center smaller. This is a first-order type of distortion; it makes a checker-board beeing imaged like a pin cushion. The opposite type of first-order distortion transforms the checker-board into a barrel.

fig.3a: object (2kByte) fig.3b: pincushion (2kByte) fig.3c: barrel (2kByte)

But when stepping from rim to center you might encounter more than one sequence  "maximum - zero - minimum"  of the scale error. Then the distortion is of second- or higher order.

Fine ... but on which parameters does the amount of distortion depend?

To put it simply: on the price of the lens system.

No fooling: minimizing the distortions is a tricky job for the lens designer. Nearly every element he uses will introduce some distortion that must be compensated with the aid of additional lens elements. Making the final design heavy and expensive.

But there is some hope for us, the lens users: Problems with distortions increase as the field angle (para. 2.2) gets wider.

So, guys, there is one simple cheap recipe against all kinds of distortions: use long, long focal lengths!

Like everywhere in an engineer's life, it's not as simple. Long focal length causes those drawbacks I already stated at the end of para.2.2. You will have to trade off distortion (or price of its correction) against size of the optomechanical setup.

In what kind of terms can we specify "distortion"? This visible (or at least measurable) property of an image should be turned into simple specifying numbers.
For example you could state: "xyz percent error in the position of any image point across the entire field".

How to measure this distortion is to be seen in the following figure by Sischka, which takes barrel distortion as an example:
fig.3d: measuring distortion (42kByte)
With the author's kind permission, I took this figure from:
"Fundamentals of machine vision lenses" by Nicholas Sischka et al. in "Vision Systems Design", Dec.2014, pp.24 ff.

With the definitions from fig.3d, you can easily calculate:

(distortion in percents) = 100 * (AD - PD) / PD

An image that is formed by a normal lens   and assessed with the naked eyball   looks pretty and will hardly reveal any distortion   --   with what magnitude of distortions will we have to cope?
Some examples:

distortion (percent)
1/3"-CCD-Lens-3,8 (f=3,8mm)
1/3"-CCD-Lens-30  (f=30mm)
less than 0.1
S5LPJ1012 (f=10mm; for 1/3")
TF2,8DA-8 (f=2,8mm;  for 1/3")
TF15DA-8  (f=15mm;  for 1/3")

(This table is not intended for directing you to some manufacturer; I recommend comparing   prices / technical data / availabilities   all through the market.)

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Last modified Feb. 27th, 2015