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. 3.1 Spectrometer optical diagram
DAY 2: SYSTEM OPTICS
3.1 Spectrometer optical diagram
3.2 Front optics
3.3 f/value of a spectrometer
3.4 Magnification of the slits
3.5 Bandpass and resolution
3.1 Spectrometer optical diagram
An optical diagram is a standard way to trace rays through a spectrometer in an unrolled linear fashion. It visualizes a center cross section of the instrument perpendicular to the slits, parallel to the axis of refraction. AS
Aperture Stop L1
Front / field lens L2
Collimator lens or mirror G
Grating L3
Focusing lens or mirror S
Area Source S1
Area of the source image S2
Area of the input slit S3
Area of the diffracted image (exit slit) p
Object distance of L1 q
Image distance of L1 f2
Entrance arm length (focal length L2) f3
Exit arm length (focal length L3) W
Half angles h
Entrance slit height h’
Exit slit height w
Entrance slit width w’
Exit slit width Wg
Width of grating Hg
Height of grating

4. DAY 2: SYSTEM OPTICS 3.2 Front optics 3.1 Spectrometer optical diagram
3.3 f/value of a spectrometer
3.4 Magnification of the slits
3.5 Bandpass and resolution
3.2 Front optics
Single thin Lens equation
Magnification
Numerical aperture
F/value or f/#

5. 3.3 f/value of a spectrometer
DAY 2: SYSTEM OPTICS
3.1 Spectrometer optical diagram
3.2 Front optics
3.3 f/value of a spectrometer
3.4 Magnification of the slits
3.5 Bandpass and resolution
3.3 f/value of a spectrometer
The f/value of s spectrometers depends on whether you watch the grating from the exit slit or the entrance slit.
Define D as equivalent diameter as
seen from slits.
The f/values are then

6. 3.4 Magnification of the slits
DAY 2: SYSTEM OPTICS
3.1 Spectrometer optical diagram
3.2 Front optics
3.3 f/value of a spectrometer
3.4 Magnification of the slits
3.5 Bandpass and resolution
3.4 Magnification of the slits
Slit height magnification from single
lens consideration gives
The grating acts as lens along the entrance slit of height h. Slit height magnification is then simply the result of a lens with object distance f2 and image distance f3.
Slit width magnification is different and is given as
This will be proven later!

7. 3.5 Bandpass and resolution
DAY 2: SYSTEM OPTICS
3.1 Spectrometer optical diagram
3.2 Front optics
3.3 f/value of a spectrometer
3.4 Magnification of the slits
3.5 Bandpass and resolution
3.5 Bandpass and resolution
Bandpass is the measure of an instrument ability to separate adjacent spectral lines. It is defined as the recorded Full Width at Half Maximum (FWHM) of a monochromatic spectral line
If F is the recorded spectrum,
B the source spectrum and
P the instrumental line profile then
- related to width of the slits, natural line width, resolution,
alignment, diffraction effects, aberrations or quality optics etc.

8. Assume resolution depends on width of slits and that the instrument is perfectly aligned.