detectors.md

include(joinpath(@__DIR__, "..", "..", "assets", "cond_save.jl"))

detector_showcase_dir = joinpath(@__DIR__, "..", "..", "assets", "detector_assets")

conditional_include(joinpath(detector_showcase_dir, "spotdetector_showcase.jl"))
conditional_include(joinpath(detector_showcase_dir, "photodetector_showcase.jl"), use_placeholder=false)
conditional_include(joinpath(detector_showcase_dir, "psfdetector_showcase.jl"), use_placeholder=false)

Detectors

In practice, photodetectors allow the conversion of electromagnetic radiation into electric signals. BMO provides the Detector as an element to capture and evaluate optical data during and after running a simulation, respectively. The Detector is designed to accumulate e.g. field or ray data, enabling analysis of intensity distributions, interference patterns, and other beam properties. Currently, post-processing capabilities are limited to the functionality as described in the Spot diagrams and Field distributions sections.

In general, detector-like elements are supposed to fall under the BeamletOptics.AbstractDetector type, which defines a interface for detector implementations.

!!! warning "Resetting detectors" In general, the data stored in a Detector is not automatically reset between calls of solve_system!. This task is placed within the responsibility of the user. A detector reset can be performed with the empty! function.

Detector type

A Detector can be easily spawned by initializing e.g. pd = Detector(5mm) which will create a 5x5 mm² detection screen.

Detector(::Real, ::Bool)
Detector

After solving a system containing a Detector, the methods listed below can be used in order to analyze the stored data. If no data is obtained during the tracing procedure, an error message will be stored.

Spot diagrams

The spot_diagram method provides a straight forward way to generate spot diagrams, which are commonly used to perform initial assessments of the optical performance of an imaging setup.

spot_diagram

Below an optical system consisting of a collection of collimated Beams passing through a ThinLens is shown. A Detector is positioned at the approximate focal plane to capture the resulting spot diagram.

The beam bundle used to generate the spot diagram was created via the CollimatedSource constructor. The resulting spot diagram of the lens shown above is visualized below.

Field distributions

Alternatively, the detector data can also be used to reconstruct electric field distributions of incoming beams on its surface using coherent addition. Depending on the beam type, either plane wave or Gaussian beam models are used. As a user, this data can be accessed using the electric_field interface.

electric_field(::Detector)

For convienience, the intensity function returns flux values directly. The optical_power method can be used in order to obtain the total optical power on the detector surface.

intensity(::Detector)

Gaussian beamlet interference

One of the use cases of the Detector is to analyse interference patterns. Below a rendered example of a detector model (FDS010) can be seen. The detector active area is marked in blue (1x1 mm²).

The figure below demonstrates an example intensity distribution captured by the detector pictured above, showing radial fringes due to a mismatch of the radii of curvature of the interfering GaussianBeamlets. In addition, the beam waists have been visualized.

!!! tip "Interferometer tutorial" Refer to the Michelson interferometer section for a detailed tutorial on how to use the Detector.

Point spread function calculation

!!! warning "Experimental feature" The point spread function estimation is a highly experimental feature. It does not use pupils (yet) but merely uses superposition of the ray-attached plane-waves. While this gives qualitatively sound results, it requires good sampling of the problem to obtain quantitatively good results. Currently no Strehl-ratio is calculated due to that.

The package offers a simple method to estimate the point spread function of a system. It is currently limited and requires careful assessment by the user, if the results are to be trusted.

To analyze the PSF of a imaging system a Detector is added to the system at the plane and orientation where the PSF is requested. This is the same approach as for the other detector types. The intensity map together with the coordinate system of the detector can be retrieved after solving the system by calling the intensity function.

!!! warning When dealing with a collimated source as the input to your optical system, where you want to calculate the PSF, DO NOT use the CollimatedSource beam group directly but instead use the UniformDiscSource constructor. This function returns a CollimatedSource with an equal-area sampling, which correctly weights the outer beams in relation to the inner beams. Otherwise the results might be wrong.

Airy-Disc Example

This is a classic example where a collimated circular beam is imaged onto a point by a singlet lens. Due to the finite size of the aperture stop (in this case given by the 15 mm size of the beam), the diffraction limited intensity pattern is given by the Airy-disc:

$$I(r)=I_0\!\left[\frac{2J_1\!\bigl(\pi D r/(\lambda f)\bigr)}{\pi D r/(\lambda f)}\right]^2$$

With r the radius from the origin, I_0 the maximum intensity, J_1 the Bessel function of the first kind of order one, D the aperture width, \lambda the wavelength and the focal length f.

# example parameters
l = 1e-3
R1 = 100e-3
R2 = Inf
d = 25.4e-3
n = 1.5
λ = 1e-6

# generate uniform source, lens and detector
cs = UniformDiscSource([0, -10mm, 0], [0, 1, 0], 15e-3, λ)
lens = SphericalLens(R1, R2, l, d, x -> n)
detector = Detector(10e-3)

# shift detector into focus
translate3d!(detector, [0, 200mm + 0.13mm, 0])

# build system
sys = System([lens, detector])

solve_system!(sys, cs)

# retrieve intensity
x, z, I_num = intensity(detector; n=500, crop_factor=10)

Visualizing the result yields the expected Airy-disk pattern.

Coma and Astigmatism Example

In this example, an aspheric lens images the collimated source onto a point but is tilted around the x-axis by 0.5 degrees. This results in aberrations distorting the stigmatic imaging and leading to coma and astigmatism.

k = -0.675
d = 75.0e-3
l = 15e-3
radius = 76.68e-3
A = [0*(1e3)^1, 2.7709219e-8*(1e3)^3, 6.418186e-13*(1e3)^5, -1.5724014e-17*(1e3)^7, -2.7768768e-21*(1e3)^9, -2.590162e-25*(1e3)^11]
AL75150 = Lens(
    EvenAsphericalSurface(radius, d, k, A),
    l,
    n -> 1.5006520430
)

xrotate3d!(AL75150, deg2rad(-0.5))

detector = Detector(15e-3)

translate3d!(detector, [0, 158.1779e-3, 0.0])
system = System([AL75150, detector])

ps = UniformDiscSource([0, -0.1, 0], [0,1,0], 0.8*d, 1550e-9)

solve_system!(system, ps)