Mads Nibe Larsen

PhD student working with hyperspectral thermal imaging

Blog posts

Flame experiments

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Hyperspectral images of flames have been acquired using the hyperspectral LWIR camera. The hope is to be able to distinguish between different kinds of fuel and identify different reaction regimes within the flames. The fuels are not premixed, meaning pure fuel is expelled from the nozzle where it then mixes with the air in order to maintain a sustaining flame (Fig. 1). Only simple and pure and fuels are used in the hope that the reactions (and hereby the spectral components) are simpler. Read more

Heated carbon composite samples

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The heating characteristics of six different carbon composite samples have been investigated by time series thermography. As depicted in Fig. 1, the samples are suspended in front of the thermal camera (not hyperspectral), and heated by a heat gun for 30 s after which the cooling is observed for 2 minutes. Initial experiments using a hot plate to heat one end of the samples were not suitable to detect the defect. This might be caused by the samples dissipate most of the heat energy before it can travel from the heated end to the defect. Read more

Summary of NMF-based reconstructions

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This is going to be a broader overview of my different efforts in the attempt to reconstruct the incident spectra based on the interferograms recorded by the hyperspectral camera. The setup has been described in further detail previously_ so here is just a very short introduction of the problem in terms of an $\mathbf{AX}= \mathbf{B}$ problem. The system matrix, $\mathbf{A}$ describes the transmission through the Fabry-Pérot interferometer at different combinations of wavelengths and mirror separations. A sensor response has been fitted an multiplied with each row of $\mathbf{A}$ (each row represent the transmission spectrum in terms of wavelengths/wavenumbers at a specific mirror separation). Each column of $\mathbf{X}$ contains the incident spectrum of the sample. This spectrum is a combination of the light source being transmitted through the material sample along with a reflection component coming from the environment. Both the transmission and reflection measurements are obtained by FTIR spectroscopy (not ATR, but two separate measurements). Finally, $\mathbf{B}$ contains the measured interferograms from the camera. However it is not the raw measurements, but a term including the reflection of imaging sensor off the backside of the scanning Fabry-Pérot interferometer (SFPI) has also been included. Read more

Estimating sensor response

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Using fast nonnegative least squares (FNNLS)

I have previously had some luck with with using fast nonnegative least squares (FNNLS) to estimate the sensor response based on empirical measurements. For this I need for formulate an $\mathbf{Ax} = \mathbf{b}$ problem for the solver. It has previously been described how to set up this problem, so I will not go into much detail here_. Just know that the $\mathbf{A}$ matrix expresses the known (estimated from FTIR) net flux (incident minus emitted), $\mathbf{b}$ is the measured interferogram (without offset - we’ll discuss that later), and $\mathbf{x}$ is the sensor response we need to solve for. Read more

Modelling the imaging system

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Modelling the imaging system can be rather complex due to many small something something and technicalities. The light hitting the sensor is dependent on both the wavelength as well as the mirror separation of the scanning Fabry-Pérot interferometer (SFPI). Furthermore, the position on the sensor also has an effect on the spectral profile. That is because the incidence angle increases as we move away from the center of the frame. A larger angle of incidence mean that shorter wavelengths are transmitted compared to normal incidence. The worst case is 17.25 º which results in 95.5 % shorter wavelengths compared to the middle. We are going to ignore this effect in this post in an attempt to reduce the complexity just a bit. Read more

Temperature trend inside the lens

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A measurement series was performed where the temperature was measured inside the lens over the span of a weekend. The K-type thermocouple was placed inside the lens placed inside the lens by guiding it through the airgap between the sensor and the frame of the camera. The camera is starting from ambient temperature and is turned on at time 0. Ignoring the first 10 hours (transient), the mean temperature was 24.9 ºC. Read more

Imaging diffraction grating

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These Friday afternoon experiment show how different transmission spectra behave when reflected off a grating. The black body is set to 500 ºC and pointed towards a reflective grating with 100 lines/mm and 27º blaze angle. The reflected light is then oriented such that most of it makes it onto the sensor. It is however evident that longer wavelengths (above 11.5 µm) are not imaged using this method. No further optics have been added to the setup, meaning that it is just the regular germanium lens, which focus the incoming light onto the sensor. Unfortunately the angle between the black body and the grating was not recorded. Below, you can see two videos scrolling through the layers of a hyperspectral data cube showing how the different wavelengths are transmitted at different mirror separations. The title above each image refer to the mirror separation and not the wavelength. This is also only a crop of the original data cube showing only the rows in which the reflected light can be seen. Read more

How to combine interferograms of different gasses… Theoretically at least

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What happens if we use the hyperspectral LWIR camera to measure a mixture of gasses? Let’s say that we know the interferograms of the gasses individually, but not their combination. We are only going to work with this theoretically, meaning that we a just going to use a system matrix calculated from TMM and only considering how different FTIR spectra will be recorded into interferograms. Read more

Calculating frequency spectrum from interferograms

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This section will be mostly a selection of assorted notes on some of my findings as I have tried to convert from the mirror separation dependent interferograms to the frequency/wavelength dependent incident spectra. There will for this reason not be any real common thread going through the text. Read more

Calculating Fabry-Pérot transmission via Net Radiation Method or the Generalized Transfer-Matrix- Method

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One of the key components to understand how the hyperspectral camera behaves is to know the transmission profile of the scanning Fabry-Pérot interferometer (SFPI). The mirrors of the SFPI consist of a 5 mm thick ZnSe substrate onto which an anti-reflective coating is deposited on one side, while a dielectric mirror is coated on the other side. The materials and thicknesses are presented in the following table Read more

Chasing the system response matrix

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A reoccurring issue is not knowing the exact response matrix of the hyperspectral camera. This matrix should describe the relationship between the mirror separation of the scanning Fabry-Pérot interferometer (SFPI), the wavelength of the incident light and the output of the camera. Knowing this would aid in reconstructing the wavelength/wavenumber dependent spectra of the incident light, which at the moment are obscured and hidden in the interferograms. Read more

Using optics to compensate spectral bending

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Two additional lenses was placed in front of the Fabry-Pérot to “colimate” the light in order to reduce the effects of spectral bending. A hyperspectral data cube of a 60 °C hotplate has been acquired both with and without compensating optics. SNV has been applied to the data cubes and a single layer of each are presented in Fig. 1. Read more

What happens if you shine a laser at the camera… (－‸ლ)

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We had received some new mirrors from a Chinese manufacturer, but it turned out that they were not good enough for use in the Fabry-Pérot. Even though they had a transmission of ≈ 15% which was as requested, the reflectance was only ≈ 65% indicating huge absorption losses. So before sending them back, I figured I would try to use them as neutral density filters and get a measurement of a 10.6 µm laser to get a feel for how the spectral resolution of the Fabry-Pérot actually is. I found a small 0.4 W L3 laser from Laser Access Company. I set the power so low that the indicator card would barely register the radiation (sensitivity of 0.05 mW/mm²). I then put one of the Chinese mirrors in front of the laser and then the hyperspectral thermal camera behind that. Even though the the light intensity should be reduced by at least 85% and by however big the absorption losses are in the Fabry-Pérot, the sensor still ended up overexposing… badly. Figure 1 illustrate the bloom effect the pixels experience in the spot, where the laser hit even after 5 minutes of relaxation time. Read more

Can a camera really be TOO fast?!

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A recent update to the thermal camera has drastically improved the speed at which it captures a thermal image. However, it might be a little too fast for it to keep up with itself. Fig. 1 illustrates the spectra of an Acktar Fractal black coated sample as well as a piece of polyoxymethylene (POM). Both Fig. 1a and 1c show the scene recorded at approximately the same mirror separation, but 1a is sampled using the ‘high mirror speed’, while 1c is captured with the ‘slow mirror speed’. The only preprocessing performed on both images is subtraction of the first band from all layers of the cube. The two do not look that dissimilar from each other, but looking at the extracted spectra in Fig. 1b and 1d, we notice a difference. The sampling points in 1b (the fast mirror speed) look more irregularly spaced compared to 1d. Read more

Black body exitance spectrum both in terms of wavelengths and wavenumbers

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A black body is an idealized object, which absorbs all incident radiation. As described by Kirchhoff’s radiation law, a black body also emits radiation at all wavelengths following Planck’s law of thermal radiation. At any given temperature and wavelength, the black body emits the highest amount of radiation possibly by any object. The spectral exitance is an expression for the total power emitted into the hemisphere per area emitter: here described in terms of wavelengths Read more

Imaging plastics - Preliminary study of PP, PE, PS and POM using hyperspectral thermal imaging

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In this experiment, a hyperspectral thermal camera (HSTC) is used to measure different kinds of plastics: Polypropalene (PP, container 1 from the wall of plastic, Polyethylene (PE, container 2), Polystyrene (PS, container 165) and Polyoxymethylene (POM, container 63). The aim is to investigate whether it is possible to extract information about their emission spectra using the HSTC and compare to absorption measurements using attenuated total reflection (ATR). Read more