The divergence of a beam can be calculated if one knows the beam diameter at two separate points far from any focus (Di, Df), and the distance (l) between these points. The beam divergence, Θ {\displaystyle \Theta } , is given by

Beam divergenceangle

In electromagnetics, especially in optics, beam divergence is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the beam emerges. The term is relevant only in the "far field", away from any focus of the beam. Practically speaking, however, the far field can commence physically close to the radiating aperture, depending on aperture diameter and the operating wavelength.

I constantly see references to video being the application where an Optical Low Pass Filter is most useful, but it seems that still images do best without one. Would it be possible to then have a camera with a sensor sans the OLPF (such as the D7100) apply the benefits of an OLPF through a special filter on the lens? Do any manufacturers make such a filter?

Beam divergenceformula

The problem with aliasing in video is to do with the method of downsampling the high resolution sensor image to produce a 1080p video frame (roughly 2 megapixels, a fraction of the resolution of modern image sensor), which uses line skipping (only reading every three or four lines from the sensor).

Angle ofdivergenceformula

Beam divergence usually refers to a beam of circular cross section, but not necessarily so. A beam may, for example, have an elliptical cross section, in which case the orientation of the beam divergence must be specified, for example with respect to the major or minor axis of the elliptical cross section.

An OLPF works by refracting the light striking it into four paths. Since theses are very tightly spaced, this has the effect of slightly blurring the image focused on the sensor just behind the OLPF. You can't detect the four different images because the size of the spread produced by the OLPF is about the same size as a single pixel well, which is the smallest unit of detection the sensor is capable of.

Ultrasonicbeam divergence calculator

where f is the focal length of the lens.[1] Note that this measurement is valid only when the beam size is measured at the rear focal plane of the lens, i.e. where the focus would lie for a truly collimated beam, and not at the actual focus of the beam, which would occur behind the rear focal plane for a divergent beam.

Like all electromagnetic beams, lasers are subject to divergence, which is measured in milliradians (mrad) or degrees. For many applications, a lower-divergence beam is preferable. Neglecting divergence due to poor beam quality, the divergence of a laser beam is proportional to its wavelength and inversely proportional to the diameter of the beam at its narrowest point. For example, an ultraviolet laser that emits at a wavelength of 308 nm will have a lower divergence than an infrared laser at 808 nm, if both have the same minimum beam diameter. The divergence of good-quality laser beams is modeled using the mathematics of Gaussian beams.

Gaussianbeam divergence calculator

In cameras without an Optical Low Pass Filter (OLPF) that are becoming more common, the high resolution of the sensor often approaches or even exceeds the resolving power of many of the lenses that will potentially be used with that camera. This means the limits of the lens itself provide the benefit of reducing moire. Reduction of moire, also known as aliasing, is the whole point of putting an OLPF, also sometimes called an anti-aliasing (AA) filter, in front of the sensor.

Most of these issues are less severe if the camera in question skips pixels to produce video at HD resolution. Since the pixel size is the same but only about every third or fourth pixel is contributing to each frame of video, the margin for error in terms of the precise amount of blur induced would be much greater. There are a few such products on the market aimed at improving the anti-aliasing performance of cameras that already have an OLPF, but they are camera (not lens) specific and tend to install in the camera's mirror box rather than attach to the lens. They usually hold the reflex mirror in the up position the entire time they are installed.

Curlcalculator

Gaussian laser beams are said to be diffraction limited when their radial beam divergence θ = Θ / 2 {\displaystyle \theta =\Theta /2} is close to the minimum possible value, which is given by[2]

Laserbeam divergenceand spot size

A better solution is to get a filter from Mosaic Engineering that mounts behind the lens, which are also specially designed for DSLR video (to provide sufficient blur for sensors that use line skipping).

If a collimated beam is focused with a lens, the diameter D m {\displaystyle D_{m}} of the beam in the rear focal plane of the lens is related to the divergence of the initial beam by

Beamdiametercalculator

where λ {\displaystyle \lambda } is the laser wavelength and w 0 {\displaystyle w_{0}} is the radius of the beam at its narrowest point, which is called the "beam waist". This type of beam divergence is observed from optimized laser cavities. Information on the diffraction-limited divergence of a coherent beam is inherently given by the N-slit interferometric equation.[2]

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This is akin to scaling images using "nearest neighbour" resampling in Photoshop (or other editing program). The gaps between the pixels that are read out is much greater than the 1 pixel blur radius of the camera's AA filter.

Beam divergence is often used to characterize electromagnetic beams in the optical regime, for cases in which the aperture from which the beam emerges is very large with respect to the wavelength. However, it is also used in the radio frequency (RF) band for cases in which the antenna is very large relative to a wavelength.

However there are after market solutions for video aliasing, including lens mounted solutions as you suggest, though I imagine the eventual blur radius will be somewhat dependent on focal length.