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.

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

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

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.

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

Etendue calculations q.e.d

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

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)

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)

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.