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linear phase iir filters

Started by shamganth August 26, 2003
Mike Rosing wrote:
> > Jerry Avins wrote:
...
> > > > That was the first instance of image stabilization I know of ... > > Hey Jerry and Keith, > > I really like this thread, and have no personal experience with image > stabilization. I was wondering if those MEMS mirrors TI makes would > work to remove air "twinkle" in an amature 'scope. You'd still need > a servo loop for tracking the center of the planet in questions, but > the tiny mirrors could be programmed by observing the previous image > and correcting for the next expected one. > > I don't know if it'd work, but it seems like you're the guys who could > do it! >
You're on to something real, but I don't think it quite does it. The MEMS mirrors have relatively large gaps between them and no particular focal length. While they might be controlled to form a semi-decent image that can be corrected for twinkle (more correctly, for the phenomena that cause it), the initial image would probably not be worth bothering to improve. Scale is important. For a small objective, atmospheric disturbances move the image whole. With a larger aperture (or the smaller cells that constitute greater turbulence), different parts of the light entering the aperture come to a focus in different places, causing the overlap of separate images. If the paths length of light from a star to different parts of the objective differ by more than about a quarter wavelength, interference effects degrade the image. Believe it or not, various schemes that servo different parts of an objective -- usually a mirror -- actually work (whoodathunkit!) with measurable success. There are even arrays of telescopes many meters apart whose images are combined with total path lengths held within a quarter wavelength. A single motion stabilizer provides real improvement of images from apertures up to 12 inches, but is barely worth while for twice that. That's why segmented mirrors are becoming pretty standard for new large installations. At least one commercial image stabilizer is available to amateurs. If I had one, I would probably rebuild the servo drivers. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Hi again

Some time ago I got the chance to talk with one of the engineers that 
was implimenting adaptive optics at Palomar.  What I found was that how 
they were going about this was fairly simple.

If Jerry and Andor were to look at an unfocused star, they would not see 
a point source, but rather a doughnut for Jerry (a schmidt cassegrain 
user) and a round ball for Andor (a refractor).  The two are essentialy 
the same excpet that the 'hole' that Jerry sees is the shadow of the 
secondary mirror.  For that matter, if Andor was to put his hand in 
front, he would see the shadow of his hand against the unfocused star. 
This springs me to what (I think) is Stupid Astronomy Trick #5.

Now put something hot, like the hand I just mentioned, on a very cold 
night, in front and watch the light bend and twist.   The bright waves 
are where the light has been bunched together, while the darker areas 
are where the light has diverged.  Its kind of like the erie effects you 
might see in a Frankenstein movie, but anyhow, thats what the problem 
boils down to.

The trick now is to unbend the light and dark patches with a deformable 
mirror controlled via a video servo loop that updates at a very fast 
rate.  A simple enough job, but somewhat specialized.

Optically you will of course want to be looking at the object in focus, 
so they use a beam-splitter to send part of the light to the adaptive 
optics and part of it to the imager.

Cheers,
Keith

> Believe it or not, various schemes that servo different parts of an > objective -- usually a mirror -- actually work (whoodathunkit!) with > > Jerry
+------------------------------------------+ |Keith Larson | |Member Group Technical Staff | |Texas Instruments Incorporated | | | | 281-274-3288 | | k-larson2@ti.com | |------------------------------------------+ | TMS320C3x/C4x/VC33 Applications | | | | $150 TMS320VC33 DSK's ARE AVAILABLE NOW | | | | TMS320VC33 | | The lowest cost and lowest power | | floating point DSP on the planet! | | 500uw/Mflop | +------------------------------------------+
Keith Larson <k-larson2@NOSPAM.ti.com> wrote in message news:<3F58A8BF.6080109@NOSPAM.ti.com>...
> Hello again Rune > > > > >>Nabbing these digitally would be a cinch, but not nearly as glamorous as > >>a photo of the planet itself. > >> > > > > Well... the chance to get images of Mars' moons don't come every day... > > it may well be seen as a greater achievement by those "in the know" than > > a nice, glamorous and stunning image of Mars itself. > > > Actually I was only referring to simply detecting the moons of Mars > using digital techniques. These moons are teeny tiny small! The planet > itself is the one to take pictures of.
I checked out Mars' moons. One measures somethink like 5 km x 8 km, the other measures some 9 km x 14 km. Not awfully large. More like asteroids than anything else.
> Somewhat related and interesting is that under the right conditions you > can image surface detail in the moons of Jupiter using amateur scopes > (check out the work by Ed Grafton). Visually seeing these moons as > distinct disks against the sky is easy at 200x and above, but visually > picking out surface detail is daunting.
What scope sizes would be needed? Is this possible at all with smaller scopes than the 36" you mentioned? It seems as if it would be very difficult to gain the light needed to get sufficient contrast, even in optimal viewing conditions.
> On the DSP side, it is worth noting that for these brighter objects > (planets) the method used is digital stabilization of the resulting AVI > file. For my program I start with centroiding followed with > correlation, but what I have found is that the correlation provides > little additional benefit (usually turned off cause its slow). The > greatest benefit comes when you can create a function that can select > the best pictures to co-register. That part has been difficult. And my > final goal is to directly attach to the video so I dont have to go to a > really crappy VCR step.
I'm not sure if I follow you here. You use a CCD to capture stills and/or video? And use some sort of correlation to enhance the images? I know some ultrasound people who used some sort of across-frames correlation measure to enhance medical images. Maybe I should try to get hold of their PhD theses...
> Another 'embedded DSP' solution that is just now beginning to catch on > is adaptive optics. By this I am not talking about the adaptive optics > that the big boys are using, but a more simplified tip/tilt/focus > arrangement.
Why not... most of the hardware is already there. Apparently, the modern astronomy scopes are fitted with motorized mounts, GPS navigators and what not, so that the user apparently only keys in what object he wants to view and waits for the scope to find it. What would be needed is an extra servo to adjust focus, some image processing capability to estimate the image quality and some feedback to control those servos. Sounds like a nice DSP hobby project. <sigh> I have to move somewhere else. Having an astronomy scope here makes only infitesimally more sense than bringing a fishing rod to the middle of Sahara: 60 clear nights per year, 40 of those during the season of the midnight sun and 15 of the remaining contaminated either by the bright moon or the aurora. Rune
Keith Larson wrote:
> > Hi again >
...
> Now put something hot, like the hand I just mentioned, on a very cold > night, in front and watch the light bend and twist. The bright waves > are where the light has been bunched together, while the darker areas > are where the light has diverged. Its kind of like the eerie effects you > might see in a Frankenstein movie, but anyhow, thats what the problem > boils down to.
To throw more light on that -- pun noted -- that's the basis of Schlieren photography. Sure, collimators and knife edges are used to increase the contrast to the point where sound waves become visible, but that's just an (analog) image-processing detail. Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Rune Allnor wrote:
> > ... most of the hardware is already there. Apparently, the modern > astronomy scopes are fitted with motorized mounts, ...
The is too much inertia even with a short-tube catadioptric system for that. Vibration is inevitable; no mount is infinitely rigid, and even slight vibration magnified a few hundred times is ruinous. Images are stabilized not by moving the scope on its mount, but by tilting a small plane-parallel plate in the image path. (For a 6- to 8-mm plate with even a short telescope, the spherical aberration introduced is imperceptible.) Mounting the tilt motors rigidly on the telescope introduces too much reaction torque for light ones like mine. A better way is to fasten the motor to a flywheel and allow it to rotate freely, with only a weak spring to establish an equilibrium DC position. There is then nothing but bearing friction to excite vibration. I should patent that, but hereby I put it in the public domain. Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Jerry Avins wrote:
>
...
> The is too much inertia even with a short-tube catadioptric system for
^ re Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
> What scope sizes would be needed? Is this possible at all with smaller > scopes than the 36" you mentioned? It seems as if it would be very difficult > to gain the light needed to get sufficient contrast, even in optimal viewing > conditions.
Suprisingly this does not require that large of a telescope. The trick is to wait for the moons to be at max distance and use an occulting bar to block the light from the planet. The limitation is not the dimness of the moons, but the glare of the planet. As an example a few other club members caught Deimos and Phobos with a 6" refractor. It is kind of like trying to spot stars in the great Orion nebula Trapezium. They are there and would be easy to see if it were not for the other stars blazing away right next door!
> I'm not sure if I follow you here. You use a CCD to capture stills and/or > video? And use some sort of correlation to enhance the images? I know some > ultrasound people who used some sort of across-frames correlation measure > to enhance medical images. Maybe I should try to get hold of their PhD > theses...
For Mars, Saturn Jupiter and the moon I capture the output of an NTSC color security camera to video tape. I then digitize this into an AVI file. Finally, I stack the images. Though I am still plunking away at a true corelator, it does not seem to be that much better than simply co-registering the centroids. I then use a 2-d filter to sharpen the results.
> Why not... most of the hardware is already there. Apparently, the modern > astronomy scopes are fitted with motorized mounts, GPS navigators and what > not, so that the user apparently only keys in what object he wants to view > and waits for the scope to find it. What would be needed is an extra servo > to adjust focus, some image processing capability to estimate the image > quality and some feedback to control those servos.
Read Jerry's post as well. He is right about not being able to use the main drive for stabilization. Too small of a correction, too much mass, too much gear reduction. BTW, there are two things to contend with... Mount/Motor vibration --------------------- These are true mechanical vibratrions that can be corrected with mechanical damping or optical path correction. Interestingly quite a bit of the mechanical problems can be dealt with mechanically, and if you can improve here, there is a lot less you need to do using brute force. I for example can see the stepper motors ticking away in my mount and am considering using rubber O-ring's to isolate them. Atmospheric turbulance ---------------------- Here nothing is vibrating, so you only option is to change/correct the optical path. You *could* attempt this with the main drive but as mentioned too many things are against you. A better solution is to mount a mirror onto a tip/tilt voice coil and move that.
> Sounds like a nice DSP hobby project. <sigh> I have to move somewhere else. > Having an astronomy scope here makes only infitesimally more sense than > bringing a fishing rod to the middle of Sahara: 60 clear nights per year, > 40 of those during the season of the midnight sun and 15 of the remaining > contaminated either by the bright moon or the aurora.
I would have to agree. Houston is a might bit warmer but ao is the humidity. I liken it to the arm-pit of Texas.
> Rune
+------------------------------------------+ |Keith Larson | |Member Group Technical Staff | |Texas Instruments Incorporated | | | | 281-274-3288 | | k-larson2@ti.com | |------------------------------------------+ | TMS320C3x/C4x/VC33 Applications | | | | $150 TMS320VC33 DSK's ARE AVAILABLE NOW | | | | TMS320VC33 | | The lowest cost and lowest power | | floating point DSP on the planet! | | 500uw/Mflop | +------------------------------------------+
allnor@tele.ntnu.no (Rune Allnor) wrote in message 

> That's a succint formulation of my immediate reaction... I always thought > that "[causal] IIR filter" and "linear phase" were contradicions in terms?
I browsed through comp.dsp after a long gap and came across this topic and the above quoted post. In case others have not already pointed this out, as the Clements paper shows, you can have causal IIR filter with precise linear phase. The catch is that the system transfer function is not rational. If one is restricted to the class of rational transfer functions, then causal, stable IIR system with precise linear phase is not possible.
Vanamali wrote:
> > allnor@tele.ntnu.no (Rune Allnor) wrote in message > > > That's a succint formulation of my immediate reaction... I always thought > > that "[causal] IIR filter" and "linear phase" were contradicions in terms? > > I browsed through comp.dsp after a long gap and came across this topic > and the above quoted post. In case others have not already pointed > this out, as the Clements paper shows, you can have causal IIR filter > with precise linear phase. The catch is that the system transfer > function is not rational. If one is restricted to the class of > rational transfer functions, then causal, stable IIR system with > precise linear phase is not possible.
What is an irrational transfer function? Surely, it can't be h(x) = x&#4294967295;sqrt(2)! Why would I care if a transfer function were rational or not? Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Jerry Avins <jya@ieee.org> wrote in message news:<3F61CC5E.BF7E91DD@ieee.org>...
> Vanamali wrote: > > > > allnor@tele.ntnu.no (Rune Allnor) wrote in message > > > > > That's a succint formulation of my immediate reaction... I always thought > > > that "[causal] IIR filter" and "linear phase" were contradicions in terms? > > > > I browsed through comp.dsp after a long gap and came across this topic > > and the above quoted post. In case others have not already pointed > > this out, as the Clements paper shows, you can have causal IIR filter > > with precise linear phase. The catch is that the system transfer > > function is not rational. If one is restricted to the class of > > rational transfer functions, then causal, stable IIR system with > > precise linear phase is not possible. > > What is an irrational transfer function? Surely, it can't be h(x) = > x&#4294967295;sqrt(2)! Why would I care if a transfer function were rational or not?
A transfer function that is rational (i.e. is a polynomial in frequency domain) separates easily into a feed-forward part and a feed-back loop. Check out the link between difference/differential equations and representations in the discrete/continuous Fourier domains. Rune