# Can average and gaussian blur be caused by optics?

I am studying Gaussian blur and average blur. I have been told that this blur can be caused by some camera effects. For example Gaussian Blur can be caused by camera jitters (fast micro vibrations)

Could this be true ? Or Gaussian blur (and the similar average blur) happens only with post-processing filters?

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While Gaussian blur (or something closely resembling it) isn't "normal", it does occur optically in specific cases. The Sony (Minolta) 135mm f/2.8 [T4.5] STF, with its apodization couplet produces something very close to a Gaussian distribution of out-of-focus blur in the "STF" range of apertures (once you stop down enough, you start to get ordinary Airy disks and convolution effects because you're not using the edges of the apodization couplet), and the out-of-focus "overlay" of lenses with significant spherical aberration (soft-focus lenses) is rather Gaussian in character as well (although the completely out-of-focus areas are more conventional).

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Are you saying out-of-focus blur is a gaussian blur? Other answers say no: photo.stackexchange.com/questions/21459/… – dynamic Mar 12 '13 at 22:14
@llnk - Where did I say that? The apodization couplet in the 135 STF is specifically designed to "de-foot" the OOF and turn it into something approaching a Gaussian distribution when the lens is nearly wide-open. Think of it as a radial graduated neutral density filter, clear in the centre transitioning to several stops down at the edges. Soft-focus lenses work by "stacking" an infinite number of images, with the in-focus image being the strongest and tailing off in intensity as focus weakens along something approximating a Gaussian distribution curve. – user2719 Mar 13 '13 at 0:14

A Gaussian blur is used to approximate the effects of many types of optical blurring. It's chosen because the Gaussian kernel is linearly separable, meaning the blur is fast to compute. It also has some useful statistical properties, but it's not designed to accurately simulate optical sources of blur.

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I disagree with both answers posted so far, they are too practical.

The question asked, whether Gaussian blur or average blur could ever be caused in-camera (as opposed to post-processing).

They can. Like the question suggested:

For example Gaussian Blur can be caused by camera jitters (fast micro vibrations)

Shake the camera either randomly with the following noise distribution, or shake it such that during exposure the camera is moved such that it is at a given position for a time proportional to the probability density function of the blur.

For the average blur, it should be a uniform distribution. For Gaussian blur, use a Normal distribution.

The average blur happens quite often, when an object is moving with a constant velocity during the exposure. (To be exact, with constant radial velocity around the nodal point of the camera, through a small angle.)

If you want to manually shake the camera to get any other blur, do it around the nodal point, and only through small angles.

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But, if you are shaking the camera, I think the blur doesn't spread the pixel in all directions like a gaussian blur, but it will blur along the direction where it was shaking the camera during exposure time... I don't think shaking camera = average or gaussian blur – dynamic Mar 12 '13 at 20:11
If you specify that you want the blur to be two dimensional you can do that too. Just move in two dimensions according to the distribution. – Unapiedra Mar 12 '13 at 20:40
Without modifying the expsoure time I don't see how I could recreate "manually" a gaussian blur. And even with a custom exposure time I think it would be almost impossible to recreate a that blur – dynamic Mar 12 '13 at 22:09
Two things: 1) Read the first sentence of my answer again. I didn't say it was easy. 2) All cameras allow the modification of the exposure time -- either automatically by the camera, or by yourself in manual or shutter priority mode. – Unapiedra Mar 13 '13 at 13:40

Blur can definitely be caused by optics, although it does not necessarily exactly conform to a Gaussian or "Average" function. Blur caused by a lens is described by its PSF, or Point Spread Function. These functions are actually quite complex, as they are convolutions of "blur" caused by multiple factors. Those factors include diffraction and a variety of different types of lens aberrations. Accurately modeling a PSF for a lens can be complicated if you do not know the exact characteristics of the lens design and the materials used in the construction of each lens element.

As far as post-processing goes, such as for the purposes of deconvolution, a Gaussian "kernel" is often used to approximate the blur caused by a lens in order to sharpen the image. More advanced kernels are used in other deconvolution algorithms that can be used to reverse motion blur or blur caused by camera shake (camera jitters), deconvolve defocus to small degrees, remove photon shot (Poisson) and banding noise with denoising and debanding algorithms in the wavelet deconvolution domain, etc.

Photographic image deconvolution is a complex field, and generally deals with what we call ill-posed problems. These problems aim to perform the inverse of a stable problem, and as such, are unstable. That means deconvolution can be effective to small degrees, but due to the potentially infinitely complex nature of the original stable problem that caused the convolution in the first place, we cannot know every factor in enough precision and detail to completely reverse the process with deconvolution, especially when the original problem is more extreme.

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Altho this is a good answer but it's a bit OT because I didn't ask for deconvolution.. But anyway we can assume that your answer to my question is No, guassian blur can't be caused by optics – dynamic Mar 12 '13 at 17:53
Well, you did ask about post-processing filters. That IS deconvolution, hence the reason I addressed that topic. – jrista Mar 12 '13 at 18:25