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, 11-13 September, 2018.

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, 11-13 September, 2018.

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

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/#

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

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!

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.

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