Optical noise

Simple way to look at it: a random baseball pitch is a single event, of a relatively large object. It's very "impulsive", in that a baseball hits with a large impulse, infrequently, which you would expect to obey a Poisson distribution.

Suppose you upped the rate, while reducing the size (so that the momentum or mass flow or something like that is more or less the same), which increases the number of particles. Consider a sand blaster: a whole lot of tiny sand particles come out, but when they individually whack into a surface, they don't make the surface go SLAP, SLAP every time, but rather it's the din of a million microscopic twacks, resulting in a dull hiss. The momentum delivered to the surface is rather constant (of course, a regular sandblaster has a lot of compressed air behind it, in addition to the sand, but hold that thought).

If you remove the sand from the compressed air, so it's just air blowing, the momentum is due entirely to the (extremely tiny, extremely numerous) molecules hitting (not even hitting at this point, rather, piling up against it and sliding away), and the amount of noise very small.

In general, the noise in a random variable goes as 1/sqrt(N) for N particles in the system (whatever that happens to mean).

Examples: A sandblaster delivering 10^6 sand grains/second is louder than a sandblaster delivering only 10^4, but not by 100 times, only sqrt(10^6/10^4) = 10 times. A number of equally powerful white noise sources, added together, has a total amplitude of sqrt(N) times (i.e., the noise per source is

You may already known all this...

Now, applying this to your case, putting more noisy current sources in parallel (equivalent to noisy voltage sources in series; either way, they add) makes the current more even. Noise is increased by a factor of sqrt(N), but the correlated signal increases by N, so the SNR goes as

In terms of correlation, the DC term is correlated, while all other frequencies are uncorrelated. So the DC term adds, while the others drop out.

Tim

If I understand things correctly what you describe is just photon shot noise or counting statistics. "Wave noise" refers to a classical intensity modulation due to beat wave frequencies. For example 10 MHz + 10.01MHz will beat at 0.01 MHz. Same thing happens in light and it should cause the intensity to have a fluctuation spectrum. A (likely too) simple argument implies that the intensity power spectrum at DC should be the same magnitude as the power spectrum at 100kHz. Now, your comment on N parallel and random current sources is noted. I thought the current output of a photodiode is a square law detection of the impinging E-field. Is this false?

Ahh, so the waves...

Well, one would expect that, if the wavefronts are uncorrelated ("white" light, after all!), then the wave noise would be similarly uncorrelated, and fluctuations would occur with a rate comparable to the bandwidth of the optical signal itself (i.e., about 300THz wide = femtosecond fringing).

Squaring is a time-domain multiplication, which means a frequency-domain autoconvolution -- essentially, the signal is shifted from "radio frequency" down to baseband, and the bandwidth doubled (which isn't really, because it goes from +BW to -BW, so it really has a bandwidth of BW again). If we start with a rectangular spectrum of "white" light from, say, red (~450THz) to blue (~750THz), it has a flat bandwidth of 300THz. Autoconvolution smears out the original rectangular spectrum into a

So, ignoring the shot noise effect, in the large-signal limit I suppose, you should get something like pink noise? Which, of course, will have a strong DC component, but the surrounding noise (assuming it's not dominated by shot noise, which is flat) should be 1/f style.

Hopefully Phil Hobbs will drop in, correcting my likely many errors. :)

Tim

Thanks Tim

This is just the argument I'm being confused by. Your pink noise = white when you chop 300 THz down to 1MHz and the power spectrum at 0Hz should for all intents and purposes be the same as at 100kHz. This clearly isn't the case for way white light is detected.

Okay, how do we sneak the large DC component in? A triangle shaped noise spectrum with a frequency base

Don't think you've made any. I'm likely missing something basic.

The fluctuations are white, but the DC is separate.

Cheers

Phil Hobbs

Hi Paul, If you are talking about wave noise ala Hanburry-Brown. Then this is very hard to see. (It would take me a bit to write down the correct equations... And then I'd still likely make a mistake :^) But the parameters include, BW of source, source size, wavlength of light, and source to detector distance. Anyway when all said and done I think this leads to (at best) a doubling of the shot noise. Your incandescent light is too broad in spectrum, and too large in area. I once spent a day trying to see the excess noise with our Rubidium lamp shinning through a very small hole from across the lab.... Didn't work. (For reasons I now uderstand.)

I've got Hanburry-Brown's book at home and I can pull the equations from that if you would like. (Maybe you can find them on the web?)

George H.

(and indeed this is one of Phil H's favorite subjects.. so he may fill in the details.)

Yes, the light slowly dawns. I think someone here posted a pdf of Hanbury Brown's book which is a real good read. I've been using octave to jinn up some band limited random phase signals. The resulting intensity power spectrum indeed has a massive DC spike for reasons that are now apparent. I think it's somewhere around chapter 4 that HB goes through wave versus shot noise in a plane wave. Based on what I've read there shot and wave noise should be about equal for a DC photocurrent of 300 uA. But alas this is for a plane wave and not my light bulb (or the sun for that matter) because light from different directions add by intensity and not by field.

So, would one stand a chance at seeing white light wave noise if one first couples the light into a fiber before going to the diode? The thought here is that I would have a spatially coherent spot on my diode so the HB plane wave argument would be closer to truth??

Thanks Paul C.

Actually, is it? The arithmetic should work at DC if it's the right arithmetic. I've done some numerical experimenting with random phase band limited signals and indeed there is a large DC spike in the power fluctuation spectrum for reasons that are apparent. My argument above must be confused somehow...

Thanks Paul C.

Chapter 4 sound right. I don't think there's any absolute current that is needed. But there is a relation between the photon flux and the bandwidth. And the signal goes as the probability that two photons arrive at the same 'time'. For this case I take the photon 'length' to be given by ~ 1 over the bandwidth.. with the appropriate scaling factors.

There's also a spatial 'overlap' condition that has to be satisfied. So that goes as the QM probability that an event (the detection of two photons) happens in two different ways. I've pictured one, one photon leaves S1 and arrives at det1 and 2 to 2. The other is that S1 goes to det2 and S2 to det1. (harder to draw.)

^ S1..........................det1 ^ | | |D d | | V S2..........................det2 V

When you work all that out. (several pages) You get a condition that D*d/L*lambda < 1 (or 1/2 maybe?) (lambda is the wavelength) Now you can think of the S's as different sources and the det's as different detectors or just the size of one source (detector.)

Well I'm sorry to say but I don't think so. (But I'm far from an expert.) I think the end of your fiber becomes the new source.... or converesly the input to the fiber is your detector. In my case I thought is was permissible to put a lens between the source and detector. I was able to get lots of light, but no excess noise. I'd still like to do this in the lab some day. Phil H. claims it's not that hard, but I think we each have different 'hardness scales'. His talc is my diamond :^)

George H.

The fluctuations are just that, fluctuations about the DC level.

Cheers

Phil Hobbs

Because there are no negative photons.

Don't forget DEDs.

Cheers

Phil Hobbs

-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics

hobbs at electrooptical dot net

Just bias an LED backwards. It will absorb photons and generate current.

--

John Larkin Highland Technology Inc

Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom timing and laser controllers Photonics and fiberoptic TTL data links VME analog, thermocouple, LVDT, synchro, tachometer Multichannel arbitrary waveform generators

It'll do that even if you don't bias it. LED->LED optocouplers are sometimes very useful.

Cheers

Phil Hobbs

also, as an extension of the concept, a bidirectional LED LED TDM link

Jure Z.

I've read about those, but never done one. I usually use them for floating sub-nanoamp current sources.

I'm doing a front end for a semiconductor equipment company just now that floats the gate of a BF862 with a suitable protection network and a highly effective bootstrap. The couple of pA of gate leakage is taken care of by back-to-back LEDs in series with back-to-back BFT25A CB junctions. The LEDs are illuminated just by being mounted next to their respective drive LEDs--a CTR of probably 1 ppm, which is much better than good enough. The net effect is an adjustable, bidirectional picoamp source.

A servo loop keeps the offset and drift at zero, except during a measurement when the loop is opened.

Cheers

Phil Hobbs

LEDs have unpredictable capacitances. Apparently similar parts may have 5 pF, or may have 80 pF at zero bias. I haven't explored their c-v curves.

or

The nice thing about the LED + BFT25A trick is that the Rx-side LED has enough open-circuit voltage to push current through the C-B junction of the transistor with no temperature gradient issues. Using a single silicon PD for that job would be much dicier.

Cheers

Phil Hobbs

I brought your frontends article and book to KT many many, moons ago, ( I used to work there) ,where it was an instant success. Are you consulting for them ?

Thanks, Jure Z.