1. BASIC HYPER SPECTRAL IMAGING
Fred Sigernes 1,2,3,4
1 The University Centre in Svalbard (UNIS), N-9171 Longyearbyen, Norway
2 The Birkeland Centre for Space Science (BCSS)
3 The Kjell Henriksen Observatory (KHO)
4 Centre for Autonomous Marine Operations and Systems (AMOS) NTNU
Lectures: TTK20 Hyperspectral remote sensing, Module 1, AMOS – NTNU, September, 2018.

2. Lecture plan: TTK20 Hyperspectral remote sensing Module 1
Instructor: Adjunct Professor Fred Sigernes
Day 1
09:15 – 11:00
Basic Spectroscopy
13:15 – 15:00
Spectral Designs
Day 2
09:15 – 11:000
System Optics
13:15 – 15:00
Throughput and Etendue
Day 3
09:15 – 11:000
Calibration
13:15 – 15:00
Imaging spectroscopy
Lectures: TTK20 Hyperspectral remote sensing, Module 1, AMOS – NTNU, September, 2018.

3. DAY2: THROUGHPUT AND ETENDUE
4.1 Definitions
4.2 Etendue
4.3 Flux
4.4 Throughput
4.5 Stray light
4.1 Definitions
FluxF is defined as the number of photons per
second emitted from a source into a solid angle Q.
Intensity I has units
Solid angle.
Radiance B is then in units of

4. DAY2: THROUGHPUT AND ETENDUE
4.1 Definitions
4.2 Etendue
4.3 Flux
4.4 Throughput
4.5 Stray light
The geometric extent (etendue) characterizes the ability of an optical system to accept light. It is a function of the area S of an emitting source and the solid angle Q its light propagates into or out of. It is defined as
4.2 Etendue
In terms of numerical aperture
Ex. Fused silica fiber with diameter of 200 mm

5. Optimized Etendue
Etendue may be viewed as the maximum geometric beam size and instrument can accept. It is a constant, and should be so throughout the instrument.

6. Etendue calculations
The front lens L1 produces an image in the entrance slit plane. Only light from the image cross section that is defined by the width and height of the entrance slit will propagate into the instrument. It is important not to overfill the field of view.
The key etendue equation becomes
From the entrance slit the etendue is expressed as
At the exit slit

7. Etendue calculations
q.e.d

8. DAY2: THROUGHPUT AND ETENDUE
4.1 Definitions
4.2 Etendue
4.3 Flux
4.4 Throughput
4.5 Stray light
4.3 Flux
Flux is defined as the radiance times the etendue
From unit calculations we see that

9. Geometric losses (aberrations)
DAY2: THROUGHPUT AND ETENDUE
4.1 Definitions
4.2 Etendue
4.3 Flux
4.4 Throughput
4.5 Stray light
4.4 Throughput
Throughput is the usable flux at the exit slit, available to the detector.
Flux at the entrance slit
Exit slit flux
Grating efficiency
Spectral radiance
Geometric losses (aberrations)

10. DAY2: THROUGHPUT AND ETENDUE
4.1 Definitions
4.2 Etendue
4.3 Flux
4.4 Throughput
4.5 Stray light
4.5 Random Stray light
The radiance of random stray light is directly proportional to
the flux density!
The random scatter flux at the exit is
The ratio of detected to random flux gives us an idea of the optical signal to noise (S/N)

11. DAY2: THROUGHPUT AND ETENDUE
4.1 Definitions
4.2 Etendue
4.3 Flux
4.4 Throughput
4.5 Stray light
4.5 Directional Stray light
There are mainly 3 types of directional stray light sources:
Incorrect illumination of the spectrometer due to overfilled optics etc.
Re-entry spectra of unwanted orders that focuses onto exit plane.
Grating ghosts and stray light due periodic machine ruling errors etc.
Solutions:
Use field lenses and aperture stops to illuminate correctly.
Use masks and side baffles on grating. Tilt detector.
Buy a new grating. Seek for an ion-etched blazed holographic grating.