Month: June 2016

Radiance and Luminance – the many funny units

In electronics, we typically have very well standardized measurement units, at least when it comes to units as Volts, Amperes, Watts and so on… However, I cannot say the same about the optics field. I have always been confused when having to deal with photometric units, but after a recent discussion with one of the camera gurus in our field, I got even more confused, which also gave the inspiration for this writing. So what is the difference between radiance and luminance and how obscure can the life of a camera designer get with such a cocktail of measurement units?

Radiance is a measure of radiometric power ꟷ it measures the rate of light energy flow. So far so good! It is (normally!) expressed in watts or joules/sec per unit area, usually steradian per squere meter.

Luminance is a measure of the power of visible light. But what is visible light? This is where things get confusing. Within Luminance, we can get (generally) two different flavours, possibly inspired by the fact that a human eye has two different photoreceptor cells:

rods ꟷ which are extremely sensitive, and can be triggered by a single photon. So at very low light levels, what we see is primarily due to the rod signal. Which also explains why colors cannot be seen at low light levels, a single photon does not carry color information.
cones ꟷ they require significantly brighter light (more photons) in order to produce a signal. And thus provide us with color information.
photosensitive gangleon cells ꟷ these were discovered recently and are responsible for our biological clock’s synchronization and I assimilate them with electronic comparators.

Okay the last paragraph drifted a bit, back to luminance, the two different flavours of it are:

  • Photopic flux is expressed in lumens and is weighted to match the responsivity of the human eye, which is mostly sensitive to yellow-green. But still? What is mostly sensitive to yellow-green? We are all different and there is no single sharp standard.
  • Scotopic flux is weighted to the sensitivity of the human eye in the dark adapted state, here as well, what is dark anyway?

Two derivatives of luminance and radiance are irradiance and illuminance accordingly. These are measures of the corresponding light flux per unit area at the receiver side. In other words, radiance is the energy radiated from the light source towards a unit area, and irradiance is the energy received without the light loss during its pathway. Typically expressed as W/m2/sr and lm/m2/sr. But there is more to it, there exist a dozen of other measurement units, and here is where you should get some popcorn and start reading or browsing around wikipeida:

Let’s start with the candela as I will have to refer everything to this unit which is part of the SI standard.

1 candela (new candela) is the intensity of a source that emits monochromatic light of frequency 540×1012 hertz and that has an intensity of 1683 watts per steradian. But why 1683 watts? The number 683 very much smells like a weak british horse’s power to me… Prior to 1948 the candela unit was not standartized and a number of countries used different values for luminous intensity, typically based on the brightness of the flame from a “standard candle”. Ha-ha-ha!

Then we start:

Nit ꟷ 1 cd/m2

Stlib ꟷ it is a unit of luminance for objects that are not self-luminous. Comes from the Greek word stilbein which means “flicker”. 1 stlib = 104 candelas per square meter

Apostlib ꟷ 3.14 apostlib = 1 cd/m2 – somebody thought that can neglect the rest of pi with an such an easy hand!?

Blondel ꟷ 1 blondel = 1/π .10−4 stlib – this unit is obviously reserved to blonde people

Lambert ꟷ 1 lambert = 1/π per candela/cm2

Scot ꟷ 1 scot = 1/10−3 .π candela/m2

Bril ꟷ 1 bril = 1/10−7 .π candela/m2

Foot-lambert ꟷ 1 foot-lambert = 1/π candela per square foot

Foot-candle ꟷ 1 foot-candle = lm/ft2

The image sensors field is baffled with all these units, some of which are still in use today. A possible explanation for why we have so many photometric units, compated to a single sharp one for electric current, is that we as humans naturally have light detectors, but not electric current ones (well, sort of). Each of us owning such receptors can create the perfect environment for speculation. This, combined with the vigorous victorian age pride is possibly the cause for the creation all those weird units. What do you think?

Lastly, here, if somebody asks you, this is one foot-candle!

One foot-candle

One foot-candle, courtesy of General Electric

 

 

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ATLAS silicon strip detectors and charge sensing

Some time ago, scientists at the Large Hadron Collider (LHC) at CERN reported the potential discovery of a new fundamental particle, which does not fit anywhere in the standard model of physics. According to “the news”, the latest data from ATLAS and CMS (LHC’s two largest detectors) shows two unexpected data “bumps” from the usual gamma-ray flashes, which are correlated and acquired from two separate detectors. According to physicists, this may point to the existence of a particle that dwarfs by light-years even the recent discovery of gravitational waves.

It is not yet sure if this measurement data would get confirmed or rejected, but the latest news point that the significance of the results is fairly low, owning a sigma of 1.6 approximately. That fact inspired me to write a bit about the basics of the basics in silicon strip detector charge sensing, which is a stone age technology in commercial light sensing CMOS image sensors nowadays.

So what are strip detectors and how are they used? These are basically PN-junctions with an extremely wide aspect-ratio and, as their name suggests, look like strips. Here’s a sketch:

A bird's eye view of silicon strip detectors

A bird’s eye view of silicon strip detectors

These strips usually share an N-type substrate while each is P+ doped, covered by aluminium with some extra insulation layers in between. The LHC scientists are interested in observing interference patterns in X and gamma rays caused by the decay of the sought after particles. Apart of their intensity, what also interests them is the spatial trajectory of the high-energy rays. In order to detect the 2D-position of the gamma rays, they have invented a very clever strip array configuration. Let me explain, here’s another sketch:

Particle incidence angle detection using parallel strip configuration

Particle incidence angle detection using parallel strip configuration

A falling particle would have a higher probability of generating electron-hole pairs in the strip which is crossed by the X-ray photon, which already creates a kind of a 1-dimensional readout. To obtain the angular information, the adjacent strips could also be read-out and a particle correlation can be reconstructed. In other words, if the gamma ray happens to fall with some angle of e.g. 45 degrees, it will thus generate electron-hole pairs in two or three adjacent silicon strips. This gives us already almost 2D particle trajectory information. However, CERN engineers have decided to expand the technique even further, by adding another cross-pair of detectors underneath the upper set:

Hybrid X- and Y- direction parallel strip sensor configuration

Hybrid X- and Y- direction parallel strip sensor configuration

That way not only they can extract position and angular information in the x-direction, but also the y-direction, which, by using some post-processing provides accurate particle intensities and trajectories. But how can these PN silicon strips be read out?

The simplest method in reading out thousands of strips, is the use of an integrated charge amplifier and digitization electronics per each channel. Charge sensitive amplifiers have not been very “widely” used in the past with passive pixel CMOS image sensors, and have proven to be very suitable for single detector readout. These are still used in single-line CMOS line scan sensors due to their low-noise capabilities for low detector capacitance.

Typically, operational amplifier-based integrators using an integrating capacitor in the feedback are a commonly used scheme which is sketched below:
A basic charge amplifier topology for strip sensor readout

A basic charge amplifier topology for strip sensor readout

These amplifiers have high input impedance, they integrate weak charge pulses and convert them into voltage pulses for amplification and then buffer the output for readout from the next block in the chain. Because of that operation, this type of amplifier is called a “charge amplifier”. The first stage of a charge amplifier is usually a low-noise differential pair and its open-loop gain is set sufficiently high so that its amplification is not influenced by the detector capacitance which reduces the gain in the feedback. The output stage is a low-impedance buffer so it could drive the next circuits in the chain, typically an S/H stage of an ADC.

When particle decay rays strike the silicon strips, signal charge pulses Qs are generated, with an amplitude proportional to the particle energy. Due to this charge generation, the input potential of the charge amplifier lifts up and during the same time, a potential with reverse polarity appears at the output, due to the negative feedback amplifier. However, because the amplifier’s open-loop gain is sufficiently large, its output potential works through the feedback loop so that it causes the input terminal’s potential drop to zero, after some settling time dependent on the unity-gain bandwidth of the opamp itself. As a result, the signal charge pulses Qs are integrated to the feedback capacitance Cf and the output’s voltage changes according to the integrated charge. At that moment, since the feedback resistor Rf for DC is connected in parallel to the feedback capacitor Cf, the output voltage slowly discharges with the time constant determined by τ=Cf · Rf. The output voltage of such a charge amplifier scheme is dampened by the size of the feedback capacitor Cf, thus Qs and Cf must be chosen wisely to fulfill the specifically desired dynamic range. As a result it can be observed that the noise performance and dynamic range of this readout scheme is of highest trade-off. Increasing the dynamic range, leads to a lower swing on the capacitor and hence increases noise, the reverse is also applicable.

Note that the ATLAS detector has a total of over 200 m2 (square meters!!!) of pure detector strips! With a strip size of 0.01mm by 40cm we get a pretty decent number of about 50 000 strips and readout channels respectively. With such a huge set of sensors both ATLAS and CMS rely on the statistical significance of their measurements and the weird correlation in the slight gamma peaks, might truly be caused by a completely new fundamental particle. However, the readout complexity of such an enormous set of sensors is colossal, which makes induction of errors a plausible explanation as well.

Fingers crossed that all the sensing electronics works flawlessly and that all abnormal peaks detected are due to a newly detected particle.