Comparing detector noise specifications

Filed under: detectors — Tags: compare, Detectivity, detector, detector noise, NEP, noise, noise equivalent power, noise power, optical noise, photodetector, signal to noise ratio, SNR, Specific detectivity — Webmaster @ 1:13 am

After having explained the causes of optical noise in detectors, I’d like in this post to define the parameters that makes it possible to compare detectors noise specifications.

Signal to noise ratio

Also noted SNR or S/N. This is defined as the ratio between the signal power and the noise power. Hence:

$\frac{S}{N}=\frac{\overline{\left|i_{s} \right|^{2}}}{\overline{\left|i_{noise} \right|^{2}}}$

Understanding the meaning of this is quite straightforward: the higher this ratio, the best signal you get. At equal input signal, the detector with the highest SNR is the less noisy one. If S/N<1, you cannot see anything, if S/N>>1, the signal is easy to pick up. As such, the signal-to-noise ratio is not a usable figure of merit of a detector. It is rather a measure of how strong your signal is compared to the “sensitivity” of your detector.

However, comparing the optical power needed to get a SNR of 1 is a step in the right direction to compare detector noise. According to the optical noise models explained earlier,

$\overline{\left|i_{s} \right|^{2}}=\left(\frac{e\eta}{h\nu}\right)^{2}\overline{P_{opt}^{2}}$

$\overline{\left|i_{noise} \right|^{2}}=\left[2e\left(\overline{i_{s}}+\overline{i_{0}}\right)+\frac{4k_{B}T}{R} \right]\Delta\nu$

Obviously, the noise depends completely on the bandwidth of the detector. This is understandable: to differentiate a true experimental result from random experimental error, you need to repeat the experiment. Translated in detector terminology, to get a better signal you need to increase the integration time of the experiment (= decrease the bandwidth).

To define a good figure of merit, it needs to show the minimum detectable optical power and not to depend on the integration time. Enters the noise equivalent power.

Noise equivalent power

Also noted NEP. This is a slightly confused definition. The initial concept is to define the noise equivalent power as the optical power which will yield a signal to noise ratio of 1. This is then the limit of what can be detected. But with this definition the noise equivalent power can only be given at a specific bandwidth (Δν enters in the expression of S/N).

Since not two detectors have the same integration time, manufacturers tend to call Noise Equivalent Power the minimum detectable power per square root of bandwidth. We will note this noise equivalent power per unit of bandwidth $NEP_{\sqrt{\Delta\nu}}$ to avoid confusion. In this situation we have then:

$\left(NEP_{\sqrt{\Delta\nu}}\right)^{2}=\frac{NEP^{2}}{\Delta\nu}=\frac{\overline{P_{opt\mid S/N=1}^{2}}}{\Delta\nu}=\left(\frac{h\nu}{e\eta}\right)^{2}\left[2e\left(\overline{i_{s}}+\overline{i_{0}}\right)+\frac{4k_{B}T}{R} \right]$

this normalised $NEP_{\sqrt{\Delta\nu}}$ only depends on the detector itself (and sometime on the ambient temperature!) and is measured in $W\cdot Hz^{-1/2}$ . The smallest the NEP, the better is the detector.

Getting back to the ambient temperature issue, the fluctuations of the ambient temperature are generally too small in comparison of the absolute temperature to introduce a bias in the comparison. However, it is true that the higher the temperature, the more noisy a detector is. For that reason some high quality detector are cooled (generally thermoelectrically but sometime with cryogenic cooling).

Detectivity and Specific detectivity

The detectivity D is defined as the reciprocal of the NEP: $D=\frac{1}{NEP}$ . Since all of parameters we defined depend on the area of the detector, in some cases this introduces a bias in the detector comparison. Thus sometime is specified a specific detectivity D* (D star), defined as:

$D^{*}=\frac{\sqrt{A}}{NEP_{spectral}}$

In fairness, I have very rarely encountered people using this specific detectivity in optical detectors.

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Noise in photodetectors

Filed under: detectors — Tags: Dark current, fluctuation, Johnson, model, noise, Nyquist, photodetector, photodiode, physics, poisson distribution, shot noise, Thermal noise — Webmaster @ 12:01 am

After my recent post on power and energy meters, I’d like to speak about the different kind of noises that affect a photodetector and how to model them.

Quantum effect and noise: the shot noise.

Fundamental physics tells us the light is made of particles (photons), which are emitted by the source at random. For that reason, the amount of photons emitted by the source (sun, bulb, laser, etc.) is not constant, but exhibits detectable statistical fluctuations. And this is in a nutshell what shot noise is. Because of its nature, it does not depends on the quality of the detector and is unavoidable. However the shot noise becomes a real issue only when the optical intensity is fairly low: in this case quantum fluctuations become much more noticeable.

The random process of light emission can generally be modelled using a Poisson distribution, the properties of which are very well known. If we note p(n) the probability that n photons arrive on the detector:

$p(n)=\frac{\bar{n}^{n}exp(-\bar{n})}{n!}$

$\bar{n}=\sum_{0}^{+\infty}{np(n)}$

$\sigma_{n}^{2}=\sum_{0}^{+\infty}{(n-\bar{n})^{2}p(n)=\overline{n^{2}}-\bar{n}^{2}=\bar{n}}$

where $\sigma_{n}$ is the standard deviation. What this means is that for 100 photons arriving on the detector, the uncertainty about the number of photon is of ±10 (±10%). If the number of photon is somewhat closer to common levels, e.g. $10^{10}$ , the uncertainty becomes $\pm 10^{5}$ , which is ±0.000,01%. It then becomes obvious that the shot noise is an issue only at low light level.

Let’s find out now what would be the fluctuations of the signal current due to the shot noise. Since each photon induce a free electron with an efficiency $\eta$ , during the time $\tau$ the number of electron produced is then $\eta\bar{n}$ . Every electron contributes to the signal current $i_{s}$ for a charge $e$ , the average value of the signal current $\overline{i_{s}}$ is then:

$\overline{i_{s}}=\frac{e}{\tau}\eta\bar{n}$ .

Fluctuation in the number of photons create a fluctuation in the signal current, and those fluctuations are characterised by the standard deviation:

$\sigma_{i_{s}}^{2}=\left(\frac{e}{\tau}\right)^{2}\sigma_{\eta n}^{2}=\left(\frac{e}{\tau}\right)^{2}\eta \bar{n}$

If we note $\Delta\nu\simeq 1/2\tau$ the bandwidth of the detector, we can find the useful formula below:

$\sigma_{i_{s}}^{2}=2e\overline{i_{s}}\Delta\nu$

And this standard deviation $\sigma_{i_{s}}$ characterise the shot noise current.

Dark current

The dark current is the constant response exhibited by a detector during periods when it is not actively being exposed to light. It is sometime classified as another type of shot noise. It is also referred to as reverse bias leakage current in non optical devices and is present in all diodes. Physically, dark current is due to the random generation of electrons and holes within the depletion region of the device that are then swept by the electric field applied to the diode.

Similarly to the photon noise, it can be modelled by a Poisson distribution, with:

$\sigma_{i_{0}}^{2}=2e\overline{i_{0}}\Delta\nu$

Let’s note that $\overline{i_{0}}$ depends from many parameters, but generally speaking:

Si photodiodes : $\overline{i_{0}}$ ranges from 1 to 10 nA
Ge photodiodes: $\overline{i_{0}}$ ranges from 50 to 500 nA
InGaAs photodiodes: $\overline{i_{0}}$ ranges from 1 to 20 nA

Thermal noise

Thermal noise, also called Johnson noise or Nyquist noise is the electronic noise generated by the thermal agitation of the electrons inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. It was discovered by Johnson in 1927 and explained by Nyquist.

A device (a photodiode for instance) thermal noise can be modelled as a voltage source $V_{th}(t)$ in series with an ideal resistor R. $V_{th}(t)$ has a Gaussian distribution with a mean value of zero. In this case,

$\sigma_{V_{th}(t)}^{2}=4k_{B}TR\Delta\nu$

Where $\sigma_{V_{th}(t)}$ is the standard deviation of the voltage, $k_{B}$ is the Boltzmann’s constant in joules per kelvin and T is the resistor’s absolute temperature in kelvins. It can also be modelled a current source $i_{th}$ in parallel with R:

$\sigma_{i_{th}(t)}^{2}=\frac{4k_{B}T}{R}\Delta\nu$

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Buying a laser power meter: check-list

Filed under: detectors, laser beam diagnostic — Tags: beam diagnostic, check-list, detector, energy meter, how to chose, laser, photodiode, power meter, Pyroelectric, thermopile — Webmaster @ 11:21 am

Because of the wide range of power and energy meter available on the market, and even more because they tend to be not totally versatile, you need to carefully examine your needs against the capabilities of the instrument you are planning to acquire. Here is a little check list to help you decide if a laser power meter or energy meter would fit your application.

Is the meter’s calibration traceable to internationally recognized standards such as NIST?
Is your laser wavelength within the wavelength range of the power meter?
What is the power range you expect to measure (highest and lowest limit)? Does it fall within the range the power meter can measure?
What is the diameter of your beam at measurement point? Do you have any control on this (using a lens for instance)? Is the power meter aperture big enough?
What is your power density (W/cm²) and energy density (J/cm²)? Is it below the damage threshold of the power meter?
Is your laser a pulsed femtosecond? If yes you will need a flat spectral response across the laser bandwidth. This may also be the case if your laser is widely tunable and you can’t adjust the wavelength setting manually, or simply if you don’t know your wavelength.
Is your laser pulsed and do you need to measure each pulse’s energy or an average power is sufficient? If the average power is enough or if you want to measure a single pulse energy, a thermopile is better. Otherwise you will have to go for a pyroelectric sensor or a specialised photodiode
Are there a lot of vibrations in your environment? If so this would rule out a pyroelectric detector.
Most power meters are sold nowadays in a set of two separate items: a display and a sensor. Make sure you order both and that they are compatible with each other
Assess what type of display you need: do you need computer connectivity, LabView compatibility, is it to go “in the field”, do you need it wireless (yes some manufacturer do that now)…

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A short review of laser power and energy measurement devices

Filed under: detectors, laser beam diagnostic — Tags: beam diagnostic, detector, energy meter, laser, photodiode, power meter, Pyroelectric, thermopile — Webmaster @ 4:01 pm

The base of laser beam diagnostic is to know how much average power you got. Available off the shelves form different manufacturers are three main type of devices, based either on a photodiode, a thermopile or a pyroelectric detector.

Of course, many factors will influence the quality of a power meter, the most important being its calibration. One should go for power meters which calibration is traceable to a recognised standard (such as NIST).

Photodiodes: precision for low power lasers.

When a photon source, such as a laser, is directed at a photodiode detector, a current proportional to the light intensity and dependent on the wavelength is created. A photodiode sensor has a high degree of linearity over a large range of light power levels - from fractions of a nanowatt to about 2 mW (this higher limit depends a bit on the photodiode). Above that light level, corresponding to a current of about 1mA, the electron density in the photodiode becomes too great and its efficiency is reduced causing saturation and a lower reading. Most manufacturers offer a removable ND filter to allow extending somewhat the dynamic range of the power meter, generally up to about a watt maximum.

Photodiodes are generally made of silicon, thus their response is typically 350-1100 nm, and can be extended to 200-1100 nm. Occasionally one can find an off the shelf calibrated germanium or InGaAs photodiode which will allow precise measurement on the 800-1600 nm range. As you can see on the picture below, the typical response curve of a silicon photodiode is highly wavelength-dependent.

Silicon reponse curve

This importance of the wavelength dependence leads to two main drawbacks: you need to have a clear idea of the wavelength of your laser, since the power meter will ask you for it and the result will depend on the answer. Plus photodiode power meters are inappropriate for broadband light sources power measurements (for instance it is not the way forward when using femtosecond lasers).

On the positive side, photodiodes are relatively insensitive to temperature fluctuations, have a very small form factor, are fast (from a fraction of a second to some tens of microsecond response time, limited by the electronic) and are insensitive to vibrations. But their main and unique advantage lies in their ability to measure very small optical power.

Some manufacturers even offer a background light cancellation feature, which uses a second photodiode placed outside of the laser beam path but close enough to the measuring photodiode. The light measured by this second photodiode is considered as the background noise and subtracted to the reading of the first one.

Thermopiles: stability for medium and high powers

Using a thermopile sensor is a very robust and well established way to measure laser energy. The underlying principle is quite simple: it uses some thermocouples to measure the temperature gradient between the point where the laser beam hit the thermopile and the periphery where the heat is dissipated using a heatsink. It is then easy to calculate the incident laser power.

Thermopiles tend to be more accurate than photodiodes, but their sensitivity is lower. This means the error is lower in percentage, but they are unable to measure low power lasers. Typically their power range can go as low as a few hundreds of microwatt while some high power thermopile sensors can measure up to nearly 10 kW. Usable wavelength range commonly span 200-20,000 nm for a single broadband sensor.

On the down side, they are slow, at generally a couple of second response time despite software acceleration. Plus, since the measurement is based on heat exchange, a quick fluctuation of housing temperature will decrease the accuracy of the result. This is an issue for instance if the beam hits the housing or if you hold a low power thermopile by hand. Keep in mind that part of the beam energy is distributed outside the defined beam diameter, and this energy can hit the housing if your beam is too large.

Due to their slow response time, they are only really capable of measuring average power. They generally have an energy mode which allow them to measure the energy of a single pulse. Interestingly, the pulse width does not really matter: however short, the energy of the pulse will produce a heat increase and thus the meter will deliver a reading. However some thermopiles are better equipped to measure short pulses with high energy: in this situation the energy needs to be absorbed in the volume of the absorber and not only on its surface, otherwise there is a possibility to damage the sensor.

Because the measurement relies on thermal exchanges, thermopile technology is quite diverse. One can find sensor specialised on short pulses, some on long pulses, some give better results at specific wavelength, some have a spectrally flat response over hundreds of nanometer allowing broadband light measurement, and some have a slightly different technology, based on a Peltier device, which allows sub-second response time.

Pyroelectric: energy and power

Some applications absolutely need a pulse-to-pulse measurement of the energy. In those situation where an average reading of the power is not enough, a pyroelectric energy meter is the way forward.

Pyroelectricity is the ability of certain materials (generally a polar crystal or a ferroelectric) to generate an electrical potential when they are heated or cooled. When a pulse of light hits the detector, it heats it up and create that electric potential. The electrical voltage read by the measuring instrument is then proportional to the energy. Average power can be calculated by the electronic.

Pyroelectric energy meters are very fast (up to tens of kHz) and very broadband (typically 200-20,000 nm). These energy detectors will also make accurate measurements in spite of changing temperature in the environment or heating of the detector.

Unfortunately they are less durable and less accurate than thermopiles or photodiodes. They are also sensitive to vibrations and can’t measure continuous light (CW lasers) nor long pulses (it typically has to be less than 10 ms, but this varies a lot from detector to detector). It also has a maximum repetition rate. Therefore they should only be used when the measure of each pulse energy is necessary.

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Understanding laser safety classes.

Filed under: laser safety — Tags: Accessible Emission Limit, AEL, laser, laser classes, laser goggle, laser hazard, laser safety, maximum permissible exposure, MPE, NHZ, non ionizing radiation protection, personal protective equipment — Webmaster @ 11:49 am

The level of laser exposure which is considered as the limit between safe and potentially harmful is called Maximum Permissible Exposure (or MPE). Maximum Permissible Exposures are set by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and are also adopted by standardisation committees.

As Maximum Permissible Exposure evaluation and the determination of hazard areas (NHZ: Nominal Hazard Zone) are quite involved, a laser safety classification scheme has been designed by international standardisation committees to help users to decide if their laser is a potential hazard. Below is a summary of the different laser classes with their description.

Class 1

Meaning: safe
Type of laser: very low power lasers or enclosed lasers.
Maximum Permissible Exposure: is never exceeded, even for very long exposure (hours), or with the use of optical instruments.
Nominal Hazard Zone: none.
Typical Accessible Emission Limit*: 40 µW for blue.

Class 1M

Meaning: safe for the naked eye only, but potentially hazardous when optical instruments** are used.
Type of laser: medium power lasers either collimated with a large beam or highly divergent.
Maximum Permissible Exposure: can be exceeded when using optical instruments**.
Nominal Hazard Zone: none for the naked eye.
Typical Accessible Emission Limit*: a laser can be classified as Class 1M if the total output power is below class 3B (0.5 W for continuous in the visible) but the power that can pass through the pupil of the eye is within Class 1.

Class 2

Meaning: safe for unintended exposure, (less than 0.25 s) but hazardous when looking at for more than 0.25 s.
Type of laser: visible (400–700 nm) low power lasers.
Maximum Permissible Exposure: are not exceeded provided the viewings are accidental only. MPE calculation assumes the blink reflex will stop the light after 0.25 s
Nominal Hazard Zone: none for accidental exposure.
Typical Accessible Emission Limit*: 1 mW for continuous lasers.

Class 2M

Meaning: safe for the naked eye when the exposure is unintended, (less than 0.25 s) but hazardous when looking at for more than 0.25 s or when optical instruments** are used.
Type of laser: visible (400–700 nm) medium power lasers either collimated with a large beam or highly divergent.
Maximum Permissible Exposure: are not exceeded provided the viewings are accidental only and only with naked eyes. MPE calculation assumes the blink reflex will stop the light after 0.25 s. Using optical instruments** might bring the exposure above the MPE as well.
Nominal Hazard Zone: none for accidental exposure to the naked eye.
Typical Accessible Emission Limit*: a laser can be classified as Class 2M if the total output power is below class 3B (0.5 W for continuous in the visible) but the power that can pass through the pupil of the eye is within Class 2.

Class 3R

Meaning: unsafe, except when handled carefully by experienced users. Accidental short exposure is considered as a small hazard.
Type of laser: low power lasers.
Maximum Permissible Exposure: can be exceeded up to 5 times.
Nominal Hazard Zone: hazard area for the eye, none for the skin.
Typical Accessible Emission Limit*: typically 5 mW in the visible.

Class 3B

Meaning: unsafe without exception, Personal Protective Equipment (laser safety goggle) must be worn within the nominal hazard zone. Focused lasers of this class are a potential fire hazard.
Type of laser: medium power lasers.
Maximum Permissible Exposure: is exceeded more than 5 times. Skin MPE is not generally exceeded, except at focus.
Nominal Hazard Zone: hazard area for the eye, none for the skin.
Typical Accessible Emission Limit*: 500 mW.

Class 4

Meaning: dangerous, Personal Protective Equipment for eyes and skin must be worn within the nominal hazard zone. Class 4 lasers are fire hazards as well. Diffuse reflections may be hazardous. Those lasers are commonly used for cutting or welding. This can create hazardous fumes. Cutting lasers generally create a small plasma which in turn emits UV light. UV light is another hazard to consider on a manufacturing floor.
Type of laser: high power lasers.
Maximum Permissible Exposure: ocular and skin MPE are exceeded. Diffuse reflections exceed the Minimal Permissible Exposure.
Nominal Hazard Zone: hazard area for the eye and for the skin.
Typical Accessible Emission Limit*: no limit.

Notes
Accessible Emission Limit (AEL): an AEL is the maximum value of accessible laser radiation to which an individual could be exposed during the operation of a laser and is dependent on the laser class. The AEL above are given as an indication for continuous lasers, but may change for pulsed lasers or infrared lasers.

Optical instruments: two types of optical instruments increase the hazard of M lasers:

instruments which will reduce the diameter of a collimated beam (telescopes, beam reducers, binoculars). This is dangerous when using lasers with large beams (>7mm) since it is likely to increase the amount of light entering the pupil of the eye.

Converging optics such as lenses, loupes, prescription eyewear… this is an increased hazard when using highly divergent beams since it will make it less divergent for the eye, allowing a greater amount of light to enter the eye.

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