Citizen science project GLORIA (GLObal Robotic-telescopes Intelligent Array) is a first free- and open-access network of robotic telescopes in the world. It provides a web-based environment where users can do research in astronomy by observing with robotic telescopes and/or by analyzing data that other users have acquired with GLORIA or from other free-access databases. Network of 17 telescopes allows users to control selected telescopes in real time or schedule any more demanding observation. This paper deals with new opportunity that GLORIA project provides to teachers and students of various levels of education. At the moment, there are prepared educational materials related to events like Sun eclipse (measuring local atmosphere changes), Aurora Borealis (calculation of Northern Lights height), or transit of Venus (measurement of the Earth-Sun distance). Student should be able to learn principles of CCD imaging, spectral analysis, basic calibration like dark frames subtraction, or advanced methods of noise suppression. Every user of the network can design his own experiment. We propose advanced experiment aimed at obtaining astronomical image data with high dynamic range. We also introduce methods of objective image quality evaluation in order to discover how HDR methods are affecting astronomical measurements.
GLORIA (GLObal Robotic-telescopes Intelligent Array) project is targeted at both professional and amateur scientists. While the first group has a particular interest in the scientific content of image data, the second group may be interested also in imaging, including imaging with high dynamic range. High dynamic range imaging (HDRi) is a very active area of research and consumer electronics market today. HDRi methods, which may be used for both multimedia and scientific image data [
Astrophotography would seem to be a natural fit for this technique, since the objects we photograph cover an enormous range of brightness, ranging from the Sun (magnitude −26) to faint nebulae and galaxies (magnitude 10 and beyond). Stellar objects like nebulae or galaxies often hide other stars that due to the low dynamic range of the image sensor disappear in many times brighter object. This problem can be solved by using shorter exposure time, but the shape and details of the object itself will be most probably missed. Another often used technique is stacking, combining of the frames with the same exposure time [
Although high dynamic range image can be captured directly using the special expensive high dynamic range sensors, these sensors are not very suitable for the scientific purposes since end user has no control over processes inside camera. Therefore, various HDR synthesis methods combining multiple low dynamic range (LDR) images, the same scene with different exposure times, were introduced in the last couple of years. Among all the methods, exposure bracketing [
The paper is organized as follows. Section
As mentioned in the Introduction, GLORIA aimed to become the first free-access global network of robotic telescopes to allow everybody around the world to do research in astronomy [
Distribution of the GLORIA telescopes.
With provided software, anybody can design a web application for conducting research into some specific astronomical issue. Applications can directly access individual components of the telescopes—cameras, focusers, and filter wheels. Citizen scientist, therefore, may implement advanced methods of image processing, like HDRi technique, which is the subject of this paper.
Astronomical image data have very specific features which make common multimedia oriented HDR methods almost unusable: The exposure values are typically very high; that is, noise in the image is increased. The noise has significant part based on photon counting (Poisson noise), the signal-to-noise ratio may be very different in different regions of the image, and also stellar object may be distorted on different frames. Image content is affected by atmospheric turbulence and cosmic rays. The telescopes (or lenses) tend to have big focal lengths; that is, photographed stellar object must be well guided during the exposure. Wide-field lenses tend to have spatially variant point spread function. Typically used 16-bit quantization increases numerical complexity and decreases efficiency of postprocessing methods. Spatial distribution of pixel intensity is nonhomogeneous and pixels are typically grouped in isolated spots—stellar objects.
The HDRi is based on the construction of the radiance map of imaged scene from a set of frames with different exposures. For detailed overview see Figure
Process of high dynamic range image creation.
Let us have a set of
Photoquantity
Let an image captured by digital camera
Basic principle of the image formation.
To map pixel values
Function
Mann et al., authors of the papers regarded as seed papers for the area of quantigraphic HDR, assumed that CFR is a gamma function [
Grossberg and Nayar showed that recovering of
While CRF is estimated, irradiance map then could be expressed as
The noise is always included in captured images and its influence can be described by well-known parameters [
These relations can be simplified when the linear camera response function is assumed. For more details about SNR in HDR, see [
To combine a set of differently exposed images of the same scene into one HDR frame, it is necessary to find correspondence between pixels in the individual exposures. Basically, the process of two or more images aligning requires choosing one of the images as a reference and finding the geometric transformation to spatially register another image to reference image. Registered images are often convolved with appropriate kernel to degrade the point spread function of the registered image to match that of the reference image. Convoluted images are also scaled to match the intensity and background sky level of the reference image [
For our purpose, we can assume that single frames in datasets will be acquired in relatively short time (i.e., as one observer session or as a batch) by using one GLORIA telescope; that is, PSF will be constant.
Since reconstructed HDR image has much larger dynamic range than most display devices, tone mapping operators (TMO) are involved in the process of image reproduction. These operators, global or local, transform dynamic range of image to dynamic range of particular display device; more about the TMO design could be found in [
For the purpose of measurement, we used GLORIA interactive experiment with the BART, telescope placed in Ondřejov, Czech Republic [
We used wide-field camera G21600 (equipped with Kodak KAF1603ME,
Galaxy M33 captured with different exposure times (BART, ASU-CAS, Ondřejov, Czech Republic).
32 s
64 s
128 s
256 s
Galaxy M101 captured with different exposure times (BART, ASU-CAS, Ondřejov, Czech Republic).
32 s
64 s
128 s
256 s
Pixel selection for the purpose of camera response calculation is a delicate matter. Apparently we need at least two differently exposed images; more are better. Selected pixels should meet the following requirements: Having a good spatial distribution. Covering the entire irradiance range in the image as well as possible. Being selected from zones with small irradiance variance.
Some sources state that, for the range of 256 values, typical for the color channel of the multimedia image, it will be sufficient to use 50 pixels to obtain an overdetermined system of equations [
(a) CRF estimation from LDR images of M33 and (b) CRF estimation from LDR images of M101.
M33
M101
For reconstruction of the radiance map, we used the procedure described by (
The central part of final HDR frame can be seen on Figure
Details of M101 galaxy captured at 512 s exposure (a) and reconstructed with high dynamic range (b).
512 s
HDR
Methods of objective quality evaluation can be divided into two major groups. The first group is classic objective method, for example, SNR or MSE, established in Section
There are two common functions for fitting stars’ profiles, according to Bendinelli et al. [
Figure
Figure
Profile of selected stellar objects. Green line for 32 s exposure, red line for 512 s exposure (overexposed), and blue line for HDR recovered shape.
Object number 1:
Object number 1:
Object number 2:
Object number 2:
Normalized histograms of objects FWHM (M101).
32 s exposure
64 s exposure
128 s exposure
256 s exposure
512 s exposure
HDR reconstruction
Normalized histograms of objects ellipticity (M101).
32 s exposure
64 s exposure
128 s exposure
256 s exposure
512 s exposure
HDR reconstruction
Normalized histograms of objects fluxes (M101).
32 s exposure
64 s exposure
128 s exposure
256 s exposure
512 s exposure
HDR reconstruction
In order to evaluate obtained frame with high dynamic range, various tests were performed. Primarily these are global statistics, which are summarized in Table
Images of galaxy M33, overall statistics.
Frame | 32 s | 64 s | 128 s | 256 s | 512 s | HDR |
|
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Number of objects | 1203 | 1543 | 1685 | 1899 | 2304 | 2289 |
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|
2.11 | 1.95 | 2.47 | 3.16 | 5.73 | 4.46 |
|
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Ellipticity | 0.18 | 0.19 | 0.21 | 0.22 | 0.31 | 0.23 |
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SNR | 0.98 | 1.38 | 3.82 | 6.43 | 8.93 | 9.73 |
Images of galaxy M101, overall statistics.
Frame | 32 s | 64 s | 128 s | 256 s | 512 s | HDR |
|
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Number of objects | 481 | 581 | 658 | 718 | 843 | 971 |
|
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|
1.91 | 1.95 | 2.02 | 2.46 | 2.73 | 3.16 |
|
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Ellipticity | 0.21 | 0.19 | 0.15 | 0.12 | 0.13 | 0.22 |
|
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SNR | 1.34 | 6.32 | 9.33 | 12.54 | 15.98 | 19.07 |
Figure
Relationship between number of stellar objects found in the image and its SNR.
According to (
High dynamic range imaging means a new opportunity for users of GLORIA, the global network of robotic telescopes. In this paper, we presented an evaluation of irradiance map reconstructed from the set of frames with astronomical content. We compared two methods of camera response function estimation and proposed simple rule, how to select pixels for the estimation from astronomical image data. Results of methods are very similar; estimation of CRF strongly depends on the data present in the dataset. It is mostly due to the fact that it is impossible to select appropriate samples from different sets of LDR frames. It should be noted that there is no significant impact of small differences between estimated CRF; the biggest influence on the quality of the resulting image has the choice of weighting function.
According to the performed tests, it seems like high dynamic range reconstruction may have a positive impact on objective quality of image data. Although HDR reconstruction is a nonlinear operation, reconstructed images kept their nature in terms of photometric and astrometric properties. Moreover, it is evident that SNR of reconstructed irradiance map is significantly better than SNR of any LDR image. The structure of galaxy in the HDR image is clearly visible, while bright stars are not saturated. Distortion of the shape of the stellar object, which is evident in the resulting HDR image, may be due to the fact that the BART telescope does not have guiding and longer exposures are a bit blurry. There is undoubtedly the need for further tests, such as inspection of noise models in LDR frames and a comparison between noise ratios of stacked images and HDR reconstructed images.
The authors declare that there are no competing interests regarding the publication of this paper.
This work was supported by Grant no. 14-25251S nonlinear imaging systems with spatially variant point spread function of the Czech Science Foundation.