# How to find the principal point in an image?

I need to find the principal point in an image. Its a point where the principal axis intersects the image sensor. Due to misalignment this point is not at the center of image always(or image sensor). I need to precisely determine its location using any of the optical methods available(if any). Any suggestions are greatly appreciated.

More information: The camera is giving me a live feed over a screen and I am able to store, analyze any part of it in real time or later.

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Depends highly on what the image is! – ptomato Jun 26 '11 at 19:18
It must only depend on the arrangement. The principle axis always goes through to the center of the lens and perpendicular to it and hence hits the same point always. – bubble Jun 26 '11 at 19:26
Really need answer for this one. My work is stuck up because of this question – bubble Jun 27 '11 at 11:41

To do this you would need to take an image of some sort of reference object, like a regular grid pattern. You would also have to know that your imaging system has some measurable field aberrations which are radially symmetric, such as distortion. Then you could do some simple image processing to locate the center of the distortion pattern.

In the case of a regular grid pattern, you would plot the positions of the grid lines in the image. With third order distortion, the grid lines should be spaced quadratically (ie. with the space between each grid line increasing linearly). The grid spacing will reach a max (or min) at the "principal point." (I use scare quotes around "principal point" because the principal point has a specific meaning in geometrical optics, and it is not the meaning used in the question here.)

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@Colin wont it require me to place this pattern perfectly parallel to the camera? – bubble Jun 27 '11 at 5:24
@bubble: Well, the pattern should be pretty close to perpendicular to the optical axis, but small errors won't have a large effect on your results. The magnitude of the error in your measurement would go like the cosine of the angular alignment error, which means that for small angles it doesn't vary much at all. – Colin K Jun 27 '11 at 13:30
@Are you suggesting to detect the maxima manually or programmatically. It will be nice if i dont have to write a program. – bubble Jun 27 '11 at 13:49
@bubble: I guess it depends how accurate you need to be. Usually this is not a critical piece of information for most imaging systems, but it depends on what you are doing with it. If you are doing research grade astronomical observation, you will generally need to calibrate your camera in great detail. If you just want to make some simple measurements, it is generally enough to know that your imaging system has relatively low distortion. – Colin K Jun 27 '11 at 14:00
@Colin while trying to do as suggested the effect of distortion is so less that I am not able to locate the distortion center manually. – bubble Jun 29 '11 at 8:56

I suggest shining a narrow laser beam along the optical axis. Just don't fry your sensor! Hopefully, the antireflective coating of the lens is not perfect, and you will be able to see on the object side two reflections of the beam: one from each side of the lens. Align the laser in such a way that both reflections come back exactly at the output port of the laser: the beam is then perpendicular to both faces of the lens, and therefore it is exactly along it's optical axis.

Now look at the image: you have one bright spot exactly at the focus.

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This works in principle, but depends on a lot of assumptions about the imaging system. If it has multiple elements, and the assembly tolerances aren't very tight, the results could be far from correct. It also requires that the aperture be large enough that a pencil beam down the center can be large enough to avoid severe diffraction effects. – Colin K Jun 27 '11 at 15:52
As soon you try fire a laser on a camera nothing is visible. Even a very small diffracted portion of light knocks out the sensing ability completely. We see all white image. – bubble Jun 27 '11 at 16:35
I must say a very intelligent reply. But it wont work – bubble Jun 27 '11 at 19:19
@bubble: Well, if the only problem is the laser being too bright for the sensor, then you could, after the alignment, dim it with some filter, like an Hoya ND400 (400x), a B+W ND3.0 (1000x) or a pair of crossed polarizers. – Edgar Bonet Jun 29 '11 at 7:53