The best method for fringe surfing is to
arrange two photodiodes so that they see opposite phases of the fringe pattern--e.g. when PD1 is on a bright fringe, PD2 is on a dark fringe.
Wire the photodiodes in back-to-back parallel (anode to cathode), and
connect this combination between the inverting input of an op amp and
ground.
Anyhow, my question is about how the control system would look like with the carrier frequency approach?
On Thursday, October 24, 2002 at 11:01:10 AM UTC+2, BS wrote:
If you need high frequency locking, I suggest you actually lock your fringes around a fixed frequency, not around a fixed position. For instance, introduce a 100Hz movement into one of the mirrors of your setup via a piezo and correct this movement with a second mirror of the setup (also on a piezo). The advantage here is that because your mirrors are already
vibrating at a 'high' frequency (but out of phase so as to cancel their movements), you get a much higher bandwith in the correction of random phase shift errors. In addition, you don't actually need to use two photodetectors (which are not so handy) but only one. A shift of the fringes in one direction then results in a decrease (or respectively increase) of the 'carrier' frequency and hence direction of the shift is known and can be corrected for.
BS.
On 2023-02-08 10:51, HoloLab wrote:
On Wednesday, October 23, 2002 at 3:38:22 AM UTC+2, Phil Hobbs
wrote:
The best method for fringe surfing is to arrange two photodiodes so
that they see opposite phases of the fringe pattern--e.g. when PD1
is on a bright fringe, PD2 is on a dark fringe. Wire the
photodiodes in back-to-back parallel (anode to cathode), and connect
this combination between the inverting input of an op amp
and ground.
Phil, that simple setup sounds very appealing but I have been
struggling to understand how that would work. Could you detail how
the "Wire the photodiodes in back-to-back parallel (anode to
cathode)" works because as I understand it, that would add the
charges measured by the two photodiodes while I would normally want
to subtract one from the other, no? Many thanks Loic
Well, it turns out that I'm still stalking these silent corridors occasionally, and glad to see visitors with actual optics to discuss. ;)
Fringe surfing is usually done naïvely by using one photodiode,
dithering around a dark fringe, detecting the fundamental component of
the resulting photocurrent with a lock-in, and feeding that back to some actuator to zero it out. (The actuator can be lots of things, e.g. a
piezo mirror in an interferometer or a current-tuned diode laser.)
The problem with that approach is that you're servoing around a point
where your SNR is zero. (Not 0 dB, _zero_, i.e. all noise and no
signal.) The error signal builds up only quadratically with mistuning,
so the null is very poorly determined, making the lock very noisy. You
can use some huge dither to get round this, but that usually screws up
the measurement in other ways.
The two photodiode approach requires a spatial fringe pattern, e.g. a slightly misaligned interferometer. If the two PDs straddle a bright fringe, subtracting the photocurrents (by wiring the PDs in parallel, usually) [*] gives a signal that goes linearly through zero when the
fringe is exactly centered. If you pick the separation right (roughly
the 70% points), you get a nice sharp null signal with lots of SNR.
Feeding back on that gives you a good locking signal without needing
dither.
AC approaches are possible but much more complicated--making a moving
fringe pattern needs an acousto-optic modulator or the equivalent, and
you need a fair bit of RF signal processing to get that right.
(It's far from impossible--I did something vaguely like that for my
thesis long ago, but it wasn't a quick or easy job.)
Cheers
Phil Hobbs
[*] The best way of wiring PDs in parallel is to wire them in series
between opposite-polarity bias supplies. ;) Either way, the currents subtract, which is the key point.
On Wednesday, October 23, 2002 at 3:38:22 AM UTC+2, Phil Hobbs
wrote:
The best method for fringe surfing is to arrange two photodiodes so
that they see opposite phases of the fringe pattern--e.g. when PD1
is on a bright fringe, PD2 is on a dark fringe. Wire the
photodiodes in back-to-back parallel (anode to cathode), and
connect this combination between the inverting input of an op amp
and ground.
Phil, that simple setup sounds very appealing but I have been
struggling to understand how that would work. Could you detail how
the "Wire the photodiodes in back-to-back parallel (anode to
cathode)" works because as I understand it, that would add the
charges measured by the two photodiodes while I would normally want
to subtract one from the other, no? Many thanks Loic
Greetings Phil and many thanks for your reply.
I will experiment with wiring the detectors in series between opposite-polarity bias supplies, seems like a simple and sound setup,
just what I needed :)
My application is about stabilizing long exposures of holography
setups; nothing new but I like to revisit things by myself.
From what I understand now:
- the single detector approach has the advantages of not requiring a
specific fringe spacing and enabling simple phase stepping the
interferometer (by inserting a bias voltage in the loop) but has the disadvantage of requiring fringe contrast calibration and is prone to
error if the laser output power varies. Here is a nice article on
that setup: https://www.researchgate.net/publication/263582518_A_Laser_Interferometer_for_the_Undergraduate_Teaching_Laboratory_Demonstrating_Picometer_Sesitivity
- the two detector approach is immune to laser output power
fluctuations but requires proper fringe spacing
In both cases I don't quite see why it is much more complicated to
introduce a (low frequency) carrier frequency in the optical setup by
means of an additional mirror on a transducer in order to improve the "reactivity" of the loop to some external vibration as suggested
above but I might be missing something.
- the two detector approach is immune to laser output powerOr else a rotation mount, so that you can match a fixed photodiode
fluctuations but requires proper fringe spacing
spacing to your actual fringes--if the diodes are dx apart, twisting the mount effectively gives you dx cos theta, which can be significantly smaller.
There's also nothing that says the diodes have to be looking at the same fringe, just that they be on opposite slopes, and that you not have a
full fringe across the diameter of the diode.
- the two detector approach is immune to laser output powerOr else a rotation mount, so that you can match a fixed photodiode
fluctuations but requires proper fringe spacing
spacing to your actual fringes--if the diodes are dx apart,
twisting the mount effectively gives you dx cos theta, which can be
significantly smaller.
Well I was thinking of using slit-style apertures in front of the
(BPW43) Photodiodes in order to optimize its efficiency, but that
would prevent rotating them. Anyhow, this is not much of an issue
since adjusting the distance between the photodiodes and a diverging
lens does the trick as well
There's also nothing that says the diodes have to be looking at the
same fringe, just that they be on opposite slopes, and that you not
have a full fringe across the diameter of the diode.
Indeed
I have started to design a circuit, partly based on the article
previously mentioned and your parallel wiring proposal of the diodes,
if you may confirm this is what you meant:
https://flic.kr/p/2og5WDR
Pretty much. You probably don't need the resistor between the PDs and
the summing junction, and the offset pot doesn't add anything useful, I
don't think.
Cheers
Pretty much. You probably don't need the resistor between the PDs
and the summing junction, and the offset pot doesn't add anything
useful, I don't think. Cheers
Many thanks. Here were my reasonings (which are likely flawed!):
- Resistor R5 between the PDs and the summing junction is there to
yield a gain equal to R4/R5
- The offset (Bias) pot is necessary because when the PDs are at
equilibrium the output of the loop is 0volts, which is not the best
working position for a piezo, since negative voltages may occur
Again, thank you for your help. Once I get a working setup I will
share it (schematics, PCB, etc)
In both cases I don't quite see why it is much more complicated to introduce a (low frequency) carrier frequency in the optical setup by means of an additional
mirror on a transducer in order to improve the "reactivity" of the loop to some
external vibration as suggested above but I might be missing something.
On Thursday, October 24, 2002 at 11:01:10 AM UTC+2, BS wrote:
If you need high frequency locking, I suggest you actually lock your fringes
around a fixed frequency, not around a fixed position. For instance, introduce a 100Hz movement into one of the mirrors of your setup via a piezo
and correct this movement with a second mirror of the setup (also on a piezo). The advantage here is that because your mirrors are already vibrating at a 'high' frequency (but out of phase so as to cancel their movements), you get a much higher bandwith in the correction of random phase
shift errors...
On Wednesday, 8 February 2023 at 15:41:42 UTC, HoloLab wrote:travelling in the wrong direction, so first you have to stop it, and then move it to the right place but you have now less time to do so (owing to time spent halting it)...
I'm possibly being thick here, and my hands on holography experience is decades out of date, but I'm struggling to find an intuitive understanding for why vibrating the mirror is better vis-a-vis random phase shifts: surely half the time the mirror is
Maybe if the vibration was mains-electricity related (motors, etc.) it would make more sense?
Thanks
Henry
On Thursday, 9 February 2023 at 07:48:59 UTC, HoloLab wrote:
In both cases I don't quite see why it is much more complicated to introduceIME "introducing" something where it wouldn't have been otherwise will always be "more
a (low frequency) carrier frequency in the optical setup by means of an additional
mirror on a transducer in order to improve the "reactivity" of the loop to some
external vibration as suggested above but I might be missing something.
complicated" than not doing so; the issue is whether the extra complication is worth it.
Are you actually limited by vibration problems?
Not really but I am currently working with photopolymer films which are very slow, potentially yielding long exposure times, which increase the chance of a random phase shift and slow thermal drifts. So I am putting a bit of energy on the fringe-locking topic :)
I've never worked with photopolymer... can it work in the Denisyuk geometry? That can be more tolerant of noise and air movement around the laser.
https://flic.kr/p/2ohYP1Y
https://flic.kr/p/2oi2uvp
https://flic.kr/p/2oi4Cqx
... If you look at the way the interference fringes move, you can guess
that the main source of vibrations is a rigid body movement of the
optical table with respect to the room, which severely degrades the
hologram quality at recording time, and which should be compensable by a fringe-locker :)
I'm probably missing something obvious, but what then are you locking to? Taking some off the ref. beam and bouncing off the wall?
Greetings, here is a video of the fringe locker in action: https://youtu.be/0IrlpE1sPkQ
And the project page: https://github.com/Loic74650/FringeLocker
This first version works ok but could certainly work better I think. In particular a more powerful output stage with a stiffer piezo would likely improve the frequency response of the control loop.
BOM total is just under USD26, so I called it the "Poor Man's Fringe Locker" :))
Many thanks for the inputs, in particular @Phil Hobbs
Cool, well done.
You need more loop gain, though--probably a good 20 dB more. It should
be able to really lock them suckas. If the loop wants to oscillate at
higher gain, you can use more feedback capacitance.
Cheers
Phil Hobbs
OK many thanks, I will try asap and report back!
Cool, well done.
You need more loop gain, though--probably a good 20 dB more. It should
be able to really lock them suckas. If the loop wants to oscillate at
higher gain, you can use more feedback capacitance.
Cheers
Phil Hobbs
The capacitance of your piezo stack is probably in the 10-nf range--it's worth measuring that, because R_out * C_piezo is probably the dominant
pole in the loop right now.
If you need any help with frequency-compensating the loop, ask.
Cheers
The capacitance of your piezo stack is probably in the 10-nf
range--it's worth measuring that, because R_out * C_piezo is
probably the dominant pole in the loop right now.
If you need any help with frequency-compensating the loop, ask.
Cheers
Hmm, you've lost me there (that's how little I know about
electronics!). What do you mean by "probably the dominant pole in the
loop right now"? I have increased the capacitance on the output low
pass and I can now increase the gain without oscillating. Now I have increased the output gain by "a lot" but somehow it does not seem to
improve much; I might be missing something
Many thanks Phil,
OK I think we are more or less on the same page but I am coming more
from the mechanics angle rather than electronics, so the semantics
could be a little different. From what I recall from my Univeristy
course in automation, a pragmatic approach to getting coarse tuning parameters for a PID feedback system is to measure the time constant
of the system, its resonance frequency (when possible), and the "Ziegler-Nichols" method lets you estimate reasonable PID parameters.
However in this case we are only dealing with a P loop so I was
thinking of just playing with the low pass filter and gain setting to
tune it. But I am likely oversimplifying the problem. And the more I
think about it the more I am thinking a pure Integrator type of loop
could be more accurate (in removing the last DC offset error but does
it really matter in my case).
Anyhow, believe it or not I don't have any instrument to measure
capacitance (please advise a good HP, Fluke or alike instrument and
will look it up on eBay) but the spec sheet of the Murata 7BB-20-6L0
piezo specifies a 10nF capacitance, a 6.3KHz resonance freuquency
and 1KOhms Resonant Impendance.
On the bench I measured a resonant frequency of the whole system as
closer to 10KHz which is surprizing as I would have expected it to
be less since we have a mass (the mirror) glued on the piezo.
Then I tried to measure the time constant of the system by inputing a
step function into the piezo and measure the output of the PDs on a
scope but alas the signal generator is completely messing up the
signal when switched on.
Analog electronics fun for you :) I will retry by plugging/unplugging
by hand a battery output into the piezo input and see if I can
measure anything on the scope.
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