# Calculating the Etendue of Bolometer Foils¶

In this demonstration we calculate the etendue of each of the bolometer foils in a camera. The camera is produced in the same way as in the Camera From Primitives demo.

A simple analytic formula for the etendue of a foil-aperture system is:

$G = \frac{A_{foil} A_{slit} \cos{\theta_{foil}} \cos{\theta_{slit}}}{d^2}$

This formula is a good approximation when the distance $$d$$ between the foil and slit is large compared with the foil area $$A_{foil}$$ and the slit area $$A_{slit}$$ (i.e. when the system is well approximated by an infinitesimal pinhole and detector), but as the foil and slit become finite in size it becomes less accurate and a full 3D treatment is required instead.

The BolometerFoil object has a calculate_etendue method which makes this very simple. All that is required is to load the bolometer geometry information and camera body into an otherwise-empty scenegraph and call the calculate_etendue method on the foil.

"""
This example demonstrates how to calculate the etendue of a detector.

The BolometerFoil object has a calculate_etendue method which we can
use to return the etendue. This requires the correct camera geometry
to be loaded, but nothing else present.
"""
import matplotlib.pyplot as plt

from raysect.core import Point3D, Vector3D, Node, translate
from raysect.primitive import Box, Subtract
from raysect.optical import World
from raysect.optical.material import AbsorbingSurface

from cherab.tools.observers import BolometerCamera, BolometerSlit, BolometerFoil

# Convenient constants
XAXIS = Vector3D(1, 0, 0)
YAXIS = Vector3D(0, 1, 0)
ZAXIS = Vector3D(0, 0, 1)
ORIGIN = Point3D(0, 0, 0)

# Bolometer geometry
BOX_WIDTH = 0.05
BOX_HEIGHT = 0.07
BOX_DEPTH = 0.2
SLIT_WIDTH = 0.004
SLIT_HEIGHT = 0.005
FOIL_WIDTH = 0.0013
FOIL_HEIGHT = 0.0038
FOIL_CORNER_CURVATURE = 0
SLIT_SENSOR_SEPARATION = 0.02
FOIL_SEPARATION = 0.00508  # 0.2 inch between foils

world = World()

########################################################################
# Build a simple bolometer camera.
########################################################################

# The camera consists of a box with a rectangular slit and 4 foils.
# In its local coordinate system, the camera's slit is located at the
# origin and the foils below the z=0 plane, looking up towards the slit.

# To position the camera relative to its parent, set the transform
# property to produce the correct translation and rotation.
camera_box = Box(lower=Point3D(-BOX_WIDTH / 2, -BOX_HEIGHT / 2, -BOX_DEPTH),
upper=Point3D(BOX_WIDTH / 2, BOX_HEIGHT / 2, 0))
# Hollow out the box
outside_box = Box(lower=camera_box.lower - Vector3D(1e-5, 1e-5, 1e-5),
upper=camera_box.upper + Vector3D(1e-5, 1e-5, 1e-5))
camera_box = Subtract(outside_box, camera_box)
# The slit is a hole in the box
aperture = Box(lower=Point3D(-SLIT_WIDTH / 2, -SLIT_HEIGHT / 2, -1e-4),
upper=Point3D(SLIT_WIDTH / 2, SLIT_HEIGHT / 2, 1e-4))
camera_box = Subtract(camera_box, aperture)
camera_box.material = AbsorbingSurface()
# Instance of the bolometer camera
bolometer_camera = BolometerCamera(camera_geometry=camera_box, parent=world,
name="Demo camera")
# The bolometer slit in this instance just contains targeting information
# for the ray tracing, since we have already given our camera a geometry
# The slit is defined in the local coordinate system of the camera
slit = BolometerSlit(slit_id="Example slit", centre_point=ORIGIN,
basis_x=XAXIS, dx=SLIT_WIDTH, basis_y=YAXIS, dy=SLIT_HEIGHT,
parent=bolometer_camera)
# 4 bolometer foils, spaced at equal intervals along the local X axis
# The bolometer positions and orientations are given in the local coordinate
# system of the camera, just like the slit. All 4 foils are on a single
# sensor, so we define them relative to this sensor
sensor = Node(name="Bolometer sensor", parent=bolometer_camera,
transform=translate(0, 0, -SLIT_SENSOR_SEPARATION))
# The foils are shifted relative to the centre of the sensor by -1.5, -0.5, 0.5 and 1.5
# times the foil-foil separation
for i, shift in enumerate([-1.5, -0.5, 0.5, 1.5]):
foil_transform = translate(shift * FOIL_SEPARATION, 0, 0) * sensor.transform
foil = BolometerFoil(detector_id="Foil {}".format(i + 1),
centre_point=ORIGIN.transform(foil_transform),
basis_x=XAXIS.transform(foil_transform), dx=FOIL_WIDTH,
basis_y=YAXIS.transform(foil_transform), dy=FOIL_HEIGHT,
slit=slit, parent=bolometer_camera, units="Power",

########################################################################
# Calculate the etendue of each bolometer
########################################################################

raytraced_etendues = []
raytraced_errors = []
analytic_etendues = []
for foil in bolometer_camera:
raytraced_etendue, raytraced_error = foil.calculate_etendue(ray_count=100000)
Aslit = foil.slit.dx * foil.slit.dy
costhetaslit = foil.sightline_vector.normalise().dot(foil.slit.normal_vector)
distance = foil.centre_point.vector_to(foil.slit.centre_point).length
print("{} raytraced etendue: {:.4g} +- {:.1g} analytic: {:.4g}".format(
foil.name, raytraced_etendue, raytraced_error, analytic_etendue))
raytraced_etendues.append(raytraced_etendue)
raytraced_errors.append(raytraced_error)
analytic_etendues.append(analytic_etendue)

########################################################################
# Plot the raytraced and analytic etendues
########################################################################

fig, ax = plt.subplots()
foil_number = list(range(1, len(bolometer_camera) + 1))
ax.plot(foil_number, analytic_etendues, label="Analytic")
ax.errorbar(x=foil_number, y=raytraced_etendues, yerr=raytraced_errors, label="Ray-traced")
ax.legend()
ax.set_xlabel("Foil number")
ax.set_ylabel("Etendue / m$^2$sr")
plt.show()


The program outputs the following text, along with a plot of the etendues. Note that the actual values may be slightly different, due to the Monte-Carlo sampling technique used.

Foil 1 raytraced etendue: 1.851e-07 +- 4e-10 analytic: 1.883e-07
Foil 2 raytraced etendue: 2.341e-07 +- 6e-10 analytic: 2.392e-07
Foil 3 raytraced etendue: 2.338e-07 +- 5e-10 analytic: 2.392e-07
Foil 4 raytraced etendue: 1.854e-07 +- 6e-10 analytic: 1.883e-07


Caption The etendue of the foils, calculated analytically and also by ray tracing. There is good agreement between the two methods, with the ray tracing method producing a slightly lower etendue value. The analytic method has been shown to overestimate the etendue when the foil-slit distance is small compared with the aperture size (see the example in the raysect documentation), which is consistent with this result.