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Converting Voltage to brightness

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Converting Voltage to brightness

Hi there,

I'm wondering if anyone knows what the relationship between a voltage/time graph and a light curve might be? How would one go about converting a voltage to a brigthness when collecting light from a variable star?




Bikeman's picture
Photoelectric effect

I'm not quite sure about the context of this question (which voltage are we talking about), but if this in any way related to a device using the photoelectric effect, then there really is no dependency of voltage to brightness!

Voltage in the classical photoelectric experiment is related to the color of the incident light, it s current that is related to brightness.  It took some time for physicists to come up with an explanation of this, until Albert Einstein found it in quantum physics at the beginning of the 20th century,

Anyway, this would allow you to measure a value that is proportional to the rate of photons per second hitting your detector. To go from there to magnitudes, you need to calibrate the detector and then take the logarithm of the count rate to translate to the magnitude scale (because on this magnitude scale, an increase of magnitude of 1 means that the star is fainter by a factor of the 5th root of 100 (in terms of photons per second your detector will receive from that star, everything else unchanged). The calibration is necessary because if your detector has a larger collecting area for photons (larger aperture in optics), it will receive more photons per second compared to the same detector with a smaller aperture. Also the efficiency of converting photons to a photoelectric current will vary for different detector designs, materials etc. 





Thanks for the information.

Thanks for the information.

What kind of calibration are you talking about?

or rather how would I go about calibrating a photo detector?

tcalderw's picture
DC Photometers

Direct current photometers convert the photoelectricly-generated current into a voltage.  The voltage can be read directly or fed into a voltage-to-frequency circuit that produces countable pulses.  Modern equipment, like the Optec SSP, does the latter.



Voltage to frequency

So if some one wanted to study the characteristics of a variable star using a direct current photometer and no voltage to frequency converter would it be possible to extrapulate characteristics such as temperature and distance?

Bikeman's picture
I think it would be usefull

I think it would be usefull to explain a bit more in detail what kind of device/hardware you are thinking of. Do you have a specific device in mind?

Anyway...once you have a device that can measure brighness of a star, you can make estimates of its temperature IF the star is reasonably well behaved, that is if it's spectrum doesn't have odd emission or absorption features. What you need to do is to measure the brighness at two different wavelengths (say blue and green, e.g. by putting filters in front of your sensor that will only let pass light of a given wavelength band) and you can then approximate the temperature from a formula based on the measurements in the two wavelengths.

Distance is different thing altogether, and is generally one of the most difficult things to measure in astronomy. There are variables of certain, special types where you can approximately tell their distance from analysing their lightcurves (plots of brightness over time), because their brighness variations will tell you something about their absolute brighness (how bright they look from a given distance), and you can measure their apparent brightness (how bright they appear to us on Earth) with your photometer, and from that you can figure out the distance. But this only works for these special variables where you have this relationship between measurable quantities and the absolute brightness. In general, for stars, you cannot deduce the distance from just looking at the magnitude or even the light curve.



Roger Pieri
Intensity vs Voltage ?

I think André is considering the two modes that are specific to photoelectric devices and photovoltaic devices. We are often using the "photoelectric" wording for both and this is somewhat confusing. The photoelectic devices are vaccum tubes and more specifically the PMT (photo-multiplier-tubes), photovoltaic devices are the solid-state sensors like CCD, CMOS or even single PIN diodes. There are some physics difference between both.

In PMT one photon liberates one electron to the vaccum (with a given probability), that electron is then multiplied by secondary emission in an avalanche from dynode to dynode depending its energy. The result is one current pulse on the anode for each detected photon (the process is very fast). The current INTENSITY of the pulse is function of the energy of the photon. By the way the PMT can be used as both a light intensity measuring device and/or a photon-counting device. 

In photovoltaic sensors the liberated electron moves at relatively low spead into the sillicon cristal and then is trapped into a potential well (or a physical capacitor in CMOS). The accumulation of electrons charges into that capacitor results in a voltage that is then amplified and converted to digital ADUs. By the way such sensors are not sensitive to the energy of the photons, they are only photon-counting devices. That makes the relative response of both techniques somewhat different, function of the wavelength of the light, the energy of photons.

As we make the measurments in specific bandwidth (filters), that are not very large, the differences between both are usually neglected. But there are cases of large differences of colors, simulations software, spectroscopy... where that difference of response should be considered and this is somewhat an issue as the original BVRI magnitudes definitions from Johnson and others have been set using PMT (and also not well characterized filters ! ). This can be corrected by some changes of the filters response (to see Bessell work / PASP).

That doesn't impact the questions from André, both current intensity of PMT or voltage output of silicon devices can be used the same way as Heinz-Bernd explained. 

Clear Skies !


My project

I appologize for the vagueness of my questions so I'll explain myself a bit,

I've actually started building a single infrared photodiode detector for a university project which I was hoping to use to gather useful data using my own telescope. My goal was to be able to actually figure out the temperature of a star using a brightness curve however I didn't realise I would need two different filters to do that so now, in the interest of time, I am hoping to atleast have something that can properly produce a light curve but at the moment all I can do is produce a voltage curve.

What you have said has actually helped, I've had a hard time actually finding information on these different relationships. I appreciate it all.






Bikeman's picture
I see, that information is

I see, that information is very helpful.

I guess what you will want to do (which will be a nice exercise anyway) is to estimate how small the electrical effects are that you would have to measure. Stars are not very bright light sources, as a rule of thumb, in the visual passband, the brightest stars will give you a flow of 1 million photons per second per square centimeter of detector aperture area. So if your telescope has an 8 inch diameter aperture, you should get around 320 million photons per second. It is useful to have in mind that at the basic level of the photoelectric effect, the photo-current is made from one electron per captured photon, so under the most ideal circumstances, we are talking about a photo-current (which can then be translated to a voltage by some electronics magic) of 320 million electrons per second for this telescope. The more familiar unit for current is the Ampere, which actually corresponds to ca   6.25 x 10^18 electrons per second .... soooo.... our best case photocurrent here is 320x10^6 / 6.25 x 10^18 Amp = 5.12x10^-11 Amp ... (please check my math here) that is about 50 pico Ampere . So very, very , very small indeed.

So it is obvious that there has to be some element of amplification that has to be put in somewhere between the sensor that uses the phototelectric effect and the readout instrument that can measure currents or voltages in a reasonable range of values.

This amplification can have multiple forms (often combined):

The photomultiplier tubes mentioned earlier provide a first stage of amplification through a cascade of electron-generating elements, so that in the end far more than one electron per photon is generated

CCD or CMOS sensors in digital cameras allow to collect photons (and thereby electrons) over a long time (the exposure time!!) and then read-out the current generated by letting the electrons (collected over a longer time) run thru your measuring electronics all at once (well, very quickly), instead of trying to measure the electons in real-time as they are flowing from the photocurrent directly.

And of course there is always the possibility to use an electronic amplifier, which can be combined with the methods given above. So teaming up with someone who knows about electronics like amplifiers might be useful for your project.

There are sensors called phototransistors, which are basically photodiodes with effectively a simple amplifier combined, but the amplification factor is only about 100 to 1000 if I remember correctly, so this will help only a little bit.






TRE's picture
Sounds like fun. When you say

Sounds like fun. When you say brightness curve, areyou thinking about measuring a blackbody curve to determine star temperature?  That would be brightness vs wavelength or frequency. Study Wiki for Wien Approximation  or Blackbody. Spectrometer would be the instrument. 

Most AAVSO folks think of a brightness curve as a star's light in a narrow band that changes over time, or brightness vs time. Commonly magnitude vs time. That is what is presented in the AAVSO Light Curve Generator, LCG. The narrow band or bands are defined by standardized band-pass filters. There are even standard filters for the infrared region.

I see an estimate of picoAmps for a bright star in this discussion. That might be a good starting point for your circuit design. Then you should learn about things like your photodiode's quantum efficiency vs wavelength, stable low noise OP amps, stable low noise power supplies, circuit board layout, etc.

Start with the spec sheet for your photodiode and dig to understand what all the specifications mean. Here is an example:

THere is a response vs wavelenght curve also. The example may not be suitable but it has many of the same specs. From that and information about the siignal source (star), you can begin design of the rest of the circuit.

Your can layout a very nice circuit board with one of the online PC board makers. They provide the software, quickly send a better board than you will find in most amatuer telescopes, and are very inexpensive.

Calibration of your instrument to standard magnitude is a project as important as building the instrument. Might be a project for the next student. AAVSO has calibration proceedures that you can read about on their site.

Good luck on the project. You should have a seasoned electronics person at the university. Use her or him. Should you hear some screaming, simply put the soldering iron down and pick it up by the other end.


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