What is convolution, or how small a beam can I measure?

One of the differences between a CCD and slit scanning beam profiler is the lower limit of beam size measurement. A CCD is limited to around 10 pixels for an accurate beam measurement. With the current CCD technology, this means that a CCD can measure a beam of approximately 40-50um diameter. A scanning slit profiler is known for being able to measure smaller beams—but just how small?
If an infinitely narrow slit is scanned across a Gaussian beam, the light intensity transmitted by the slit as it moves across the beam will exactly map out the Gaussian profile. However, a slit of finite width is required to transmit a measurable amount of light, and the width of the slit has a detectable effect on the shape and width of the measured intensity profile. The effect of finite slit widths on beam profile measurements is explained in the following paragraphs.
The beam width is measured between the points where the intensity falls to a fraction, p, of the peak intensity at the center. The most commonly used values are p=0.5 for the full width at half-maximum (FWHM ), and p=0.1353 at the 1/e² diameter. The measured profile M(z) is similar in shape to the Gaussian profile G(z), and M(z) approaches G(z) ratio of the slit width to the measured width approaches zero. For any given slit width, the width of the measured profile M(z) is greater than that of the true profile G(z). This discrepancy becomes greater as the width of the slit increases. As a matter of convenience we consider that this error, called convolution error, is negligible (<2%) as long as the measured beam width is greater than four times the slit width. This means that for a 5um slit, the minimum beam size is around 20um; for a 2um slit, 8um.
Remember, using a slit that is smaller than you need for your beams size does not improve performance or resolution. We have found that unless you are measuring the extremely small beams, less than 20um diameter, the 5um slits are the best choice.