summary
Sending analog audio signals a few meters over shielded coax cable is a solved problem.
If your signals are limited to 3200Hz and you need 8 or 10 bits of precision per sample, then I would be pretty comfortable using standard audio coax cable to send the raw analog signals.
That might be the lowest-cost, lowest-battery-power way to handle things.
If you require DC-accurate readings at 3200Hz and 20 or 24 bits of precision per sample, shipping analog signals over even 2 meters of cable is basically impossible at any price.
If you need that precision, you are forced to digitize the signals right at the source, and ship them over the cables in some digital format.
details
Transmitting in digital format generally requires one to spend a little more money on electronics at each sensor, but it allows you to save a little money on lower-cost UTP cables and low-cost connectors.
In a few cases, transmitting in a digital format lets you use fewer cables -- a single daisy-chain through each sensor ending at the host, where each sensor forwards data from the "upstream" sensors "downstream" towards the host computer, as well as sending its own data "downstream" towards the host computer on the same cable. With an analog system, you are pretty much forced to run an independent wire to each sensor -- analog multiplexing techniques end up costing more than digital multiplexing techniques.
As the bandwidth goes up, or the desired precision of the signals goes up, or both, analog cables need more and more shielding (i.e., get more expensive) to block outside interference and cross-interference.
Eventually you reach a point where it's basically impossible to put enough shielding on a cable to get the desired bandwidth and precision.
Suggestion
Post a new question something like "I have a bunch of (insert name here) digital sensors that I want to distribute over a large area of a few meters, but I don't want to run dozens of digital control wires per sensor back to my host MCU. What's a reasonably low-cost, low-energy digital circuit I can put to reduce the number of wires I need to run to each sensor? I might be willing to run a full 4-pair CAT5 cable to each sensor to carry power + data, but no more!
Ideally much less -- is it possible to share one 4-pair CAT5 cable among 2 or 3 sensors to carry power + data?"
If you are willing to spend a few extra bucks on digital chips in order to avoid the hassle of programming a MCU at each remote location, please specify "without a MCU" (like How to decode morse code with digital logic ).
It's possible the resulting circuit may give you the full precision available from your (insert name here) digital sensors, but have a net cost less than an analog-signal system, when you balance the extra digital electronics and the low-cost unshielded cables and connectors vs. the lower analog electronics cost and the higher shielded cables and connectors.
As many suggested - first check that the source is not an optical input from celling lights, but you would see the noise without the resistor as well (assuming conditions were the same).
Your circuit uses NTV0505MC DC/DC converter, it is not an LDO so it produces ripple. In original circuit design the PSRR characteristic of the LTC2055HV suppresses this ripple by a factor of 130dB. When you add the 10M resistor - you inject this ripple straight into the first stage of signal processing line. 10M with 100k of TIA stage forms an "inverting op-amp circuit". So the ripple (or whatever you have on -5V rail) is attenuated by 1/100 factor and added to whatever useful photo-current you get from PSD pin multiplied by 100k TIA feedback. If it is not a DC/DC converter ripple - checkout the shielding of your supply rail. Supply rail may function as antenna picking up EMI emitted by surrounding power wiring.
Also to me it seems wasteful to use second OpAmp as simple unity gain buffer before the multiplexer. When working with such noisy devices as photodiodes - you would always want to do as much filtering as possible. PSD has large area (so high capacitance), that means with typical TIA design you will not get anything beyond 10kHz from it. So using second OpAmp as 2-nd order 10kHz LPF would be very beneficial to the resulting SNR.
On my practice I was picking up the PWM noise from brushless motor of the stabilizer gimbal on which the photodiode sensor was mounted. While the whole signal conditioning circuit was shieled inside a metal case, the photodiode casing itself (biased cathode) was exposed outside (or actually inside the surrounding plastic mount of the lens in front of it). With 10MOhm TIA feedback the noise was 10x stronger than the signal itself. Problem was solved with proper shielding to ground of the plastic lens mount using nickel conductive spray paint from MG Chemicals. So the only opening in EMI shield of the whole sensor was an optical lens in front of photodiode.
Best Answer
The detector is a phase detector. It tells you on the diagram that its output is Ksin(theta-phi), the sine of the angle error, which for small errors is more or less the error itself.
This is used to complete the phase locked loop, which drives the angle estimate to be equal to the input angle. The integrator is used so that any small error does not persist, but builds up until it gets corrected. It effectively gives it infinite gain at DC.