Title: Response of QD to structured beams via convolution integrals,
Abstract: We propose a new expression for the response of a quadrant detector using
convolution integrals. This expression is easier to evaluate by hand,
exploiting the properties of the convolution. Computationally, it is also
practicable to use since a large number of computer programs can right away
evaluate convolutions. We use the new expression to obtain an analytical form
of the response of a quadrant detector to a Gaussian beam and to
Hermite-Gaussian beams in general. We compare this analytic expression for the
response for the Gaussian beam with the approximations from previous studies
and with a response obtained through simulations. From the response, we also
obtained an analytical form for the sensitivity of the quadrant detector to a
Gaussian beam. Lastly, we demonstrate the computational ease of using our new
expression for the response calculating the sensitivity of the quadrant
detector to the Bessel beam.