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Characterization of cameras and time acquisition
As stated before, it is critical to have trusted fast cameras and reliable time registration in order to reconstruct the 2D shadow of distant bodies from stellar occultations.
The Lucky Star project considered the acquisition and deployment of several occultation kits, with each kit consisting of camera, time registration system, acquisition software and various optical and mechanical adapters.
In that context, this chapter describes my role in this project and the tests/validations that I performed in those kits.
The tests have as main goals:
• evaluate and validate the performances of alternative camera models un-der typical conditions,
• evaluate the accuracy of the time registration system,
• evaluate the adequacy of the acquisition software.
I performed tests in the laboratory and on the sky and involved interac-tions with the software manufacturer in order to solve flaws and to put in adequation the software and the needs of the project. The tests also con-sider the re-evaluation of kits already in use by the project(called here-on the « Merlin kit »), in particular, their time registration. Part of the data analyzed in this thesis was taken with several of those kits and the results of some tests were incorporated in the data analysis (see Chapter 3).
For portable cameras it is commonplace to use fast Charged Coupled Devices (CCD) which can reach fast readout rates of several images per second with dead times of fraction of a second (corresponding to readout and writing). In particular, Interlined CCDs reach dead times below the millisecond. Similarly, the lower prices of CMOS-based cameras make them attractive for these applications, having dead times comparable to those of CCDs.
However, the main disadvantages of CMOS against CCDs cameras are the smaller size of pixels and higher readout noises. Both effects combined can reduce the SNR obtained under equivalent conditions, as the stellar light is spread among a larger number of more noisy pixels. Nonetheless, current performances and prices make both alternatives comparable in terms of price versus performance, so that favoring one over the other is not a simple task.
Note. — (a) EMgain is the Electro-multiplication factor which can be changed from the acquisition software. When no EMgain is applied, the camera behaves as a regular CCD. (b) Relative to ambient temperature.
After an initial round of evaluation (out of the scope of this work and not described here), the decision of which camera to include in the kits was nar-rowed down to two alternatives. The first-one is the Kite camera, based on an Electro-multiplied CCD (EMCCD) from the Raptor Photonics company, and the ZWO ASI178MM-Cool camera, a CMOS-based from ZWOptical. The main differences between these two cameras are the smaller pixel size of the CMOS, the electro-multiplication and possibility of external trig-ger in the Kite, and the different interfaces between PC and camera (see Table 2.1). The electro-multiplication is an extra stage of amplification in-troduced in the camera before the signal is digitized. The main effect is to decrease the effective readout noise (RON). The electro multiplication factor can be changed from the acquisition software trough a ’EMgain’ pa-rameter going from a minimum of 0 (the camera behaves as a regular CCD) to a maximum of 3500. The relation between the gain parameter and the electro-multiplication factor is derived below as well as the reduction of the readout noise as a function of the EMgain applied.
With respect to the time registration, the Kite presents the advantage that each image acquisition can be triggered from an external signal.
Combined with an external device as the TimeBox (see below), it can provide an accurate time stamping for each image. However, the accuracy achieved with the CMOS camera is good enough for most applications and the lack of external trigger is not a limitation to achieve the scientific goals of the project (see Section 2.3).
Conversion factor and read-out noise
Both cameras were tested to determine the conversion factor g and read-out noise (RON) for different configurations. The factor g gives the conversion between the number of electrons e− recorded by the camera into digital counts, or Analog-Digital Units (ADUs), in the recorded image. The factor g is expressed in electrons per ADU (e−/ADU). This basic quantity is used below to express the RON in comparable units (i.e. e− ) so the performances of both cameras can be consistently compared. Knowing g, it is possible to estimate the SNR given a star magnitude, a telescope collecting area, and the sky brightness. In practice, several other conditions will determine the final SNR achieved in a particular observation. Among these are the star altitude, the star color, the moon light background, linked to its phase and angular distance from the star, the seeing, telescope shaking by wind, to name some. However, it is useful to have some quantitative way to compare the expected performances of the cameras under typical conditions.
The conversion factor g is calculated using the ’photon transfer curve’ (PTC) (Janesick, 2001) which basic steps are summarized here. The camera is illuminated by a source of white light with constant and uniform intensity. A centered squared region of each image is used and the rest of the image is discarded. This is done to take only the region with the most uniform illumination, and to avoid the so-called ’amplifier glow’ typically present in the borders of CMOS-based cameras. Images are taken with the acquisi-tion software ’Genika Astro’ by Airylab using different level of illumination, starting from no light (detector totally covered) and increasing the illumi-nation level up to the saturation of the detector. This is repeated changing the parameters of interest in each camera such as CM OSgain (respectively EMgain for the EMCCD camera) and binning factor.The tests were per-formed at room temperature of ∼20 C, keeping the detector temperature constant with the camera cooling system activated.
With the images acquired, the average signal S in units of ADU is calcu-lated. Then, the same images with same level of illumination are taken in pairs and subtracted to each other, and from the difference-image the vari-ance σdiff2 is calculated. Subtracting pairs of images eliminates the effect of pixel-to-pixel variations leaving only the photon noise. The variance in the original image is calculated as σ2 = σdiff2 /2 where it is assumed that noises add in quadrature. Then, from a plot of σ2 vs S the slope m is obtained using a linear fit. From that, the conversion factor g is:
Given some differences in the cameras, the procedure and results for each are explained separately.
CONVERSION FACTOR AND READ-OUT NOISE
CMOS camera
The CMOS camera permits to change a gain factor (CM OSgain) as well as a gamma factor. The CM OSgain have a direct impact in the amount of readout noise (see Table 2.2). On the other hand, the gamma factor introduces a non-linearity in the relation between the incident light and the signal in ADUs (see Figure 2.1). This is useful in some applications1 but obviously unwanted in the case of stellar occultations, e.g. for analyzing tenuous atmospheres or diffraction effects by airless bodies and their rings. In that case, the retrieval of physical parameters of the body under study (e.g. atmospheric density profiles or ring optical depths) are directly linked to the linearity of the device.
readout noise change in a factor of ∼ 2 as a function of the CM OSgain and stay roughly constant for CM OSgain > 250. The tests showed that the binned (2×2) pixel value (in ADUs) is the average of the four original pixels. This reduces the RON measured in ADUs by half but increase the RON in electrons by 2 Similarly, the RON roughly increases by a factor of 2 between binning 2×2 and 4×4. This is the expected behavior if the noise of the binned pixel is the addition, in quadrature, of the noise of the original unbinned pixel.
EMCCD camera
The EMCCD Kite camera possesses an Electro-multiplication stage that multiplies the collected charge in each pixel before the signal is digitized. When no electro-multiplication is applied, the Kite behaves as a regular CCD, so that the conversion factor g is obtained from the PTC as explained before. With the electro-multiplication applied, the slope m of the PTC gives the electro-multiplication factor g(EMgain).
Table of contents :
1 Introduction
2 Characterization of cameras and time acquisition
2.1 Conversion factor and read-out noise
2.1.1 CMOS camera
2.1.2 EMCCD camera
2.2 Dead times
2.2.1 CMOS camera
2.2.2 Kite camera
2.3 Accuracy of time registration
2.4 Test at the sky and SNR estimation
3 Physical characterization by stellar occultations
3.1 2007 UK126 and 2003 AZ84
3.1.1 Stellar occultation by 2007 UK126
3.1.2 Stellar occultation by 2003 AZ84
3.2 Size and shape from multi-epoch stellar occultations
3.2.1 Body models
3.2.2 Bayesian approach
3.2.3 Shape and size of the Centaur object (10199) Chariklo
4 The dynamics of rings around a non-spherical body
4.1 Two simple cases of non axisymmetric potential
4.2 Lindblad resonances
4.2.1 Single-mass anomaly
4.2.2 Triaxial ellipsoid
4.2.3 Summary of the section
4.3 Corotation resonance
4.3.1 Azimuthal dependence of the corotation potential
4.3.2 Stability of the corotation fixed points
4.4 Evolution of a debris disk: Lindblad resonances
4.4.1 Torques at Lindblad resonances
4.4.2 Angular momentum deposition
4.4.3 Truncation of the disk
4.4.4 Clearing the corotation zone: time scales
4.5 Applications to Chariklo’s ring system
4.5.1 Lindblad resonances
4.5.2 Corotation resonances
4.6 Discussion
5 Conclusions
