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Optics and laser beam width, need help please.

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Patrick

Mon Nov 26 2012, 04:43AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

im trying to figure out how to caluclate a laser/lens configuration. And i need help.

I want to shoot a laser line 1.9mm wide at a wall 2.9m away. then have the light bounce about 180 degrees back but now through a lens, and behind the lens a pixels sensor, with pixels only 4um wide.

how can i calculate this?

Pic to follow:

Look at the yellow arrow and circle...
(oops! it should say: "How wide will the beam be here?" )

Is it just a matter of similar triangle theorem? And proportionality of the viewable area?

...

Mon Nov 26 2012, 05:51AM

Registered Member #56 Joined: Thu Feb 09 2006, 05:02AM
Location: Southern Califorina, USA
Posts: 2445

In short, not its not that simple and to solve it exactly you need to do some more or less impossibly hard math (ex, convolve with the fresnel kernel see

The good news is that since your pixels are quite a bit larger than your wavelength (assuming .8um illumination) you can do pretty well using ray tracing methods, and there are a lot of those out there. If you really want to go nuts, OSLO is free for educational use, albeit it takes a while to get used to it.

What I don't understand is why do you have your sensor way far away from the focal point? If you want to make use of your 4um pixels you are going to want the optical system more or less diffraction limited, as drawn the lens is just going to scramble the image (it is not in an imaging configuration). Keep in mind that as you go from having a lens with the object at infinity and the image (detector) at 1 focal length behind the lens (imaging configuration) to having the object at 1 focal length in front of the lens and leaving the detector at the same spot (1 focal length behind the lens, fourier transform condition) you will go from having an imaging system to having a system which gives you the fourier transform of the image!

Patrick

Mon Nov 26 2012, 05:59AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

the 2060 pixels are 4um wide and thus about 8.3mm long

this is whay i chose the optical configuration as i did:

Panavision DLIS family Data Sheet. (DLIS-2k)

Electro-Optical and physical configuration of the would-be sensor.

its a lidar type config, but i dont have any idea what im doing, really.
Im in far over my head...

can you elaborate on ray tracing methods please?
Ah, crap! ->

Pinky's Brain

Mon Nov 26 2012, 03:49PM

Registered Member #2901 Joined: Thu Jun 03 2010, 01:25PM
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Posts: 837

You don't have a beam at the sensor, you have a defocused image.

In the end the thin lens equation is all you need ... but that doesn't really solve your problem, which is that you have conflicting goals between magnification and depth of field. Your depth of field has to be large (so a focal length << minimum working distance, with the sensor at the focal plane) but this might decrease magnification too much to fill the sensor for the arc you want to measure (as well as decreasing the lens size you can use for a single lens). You're probably going to need a lens system (also a lenticular or rod lens in front of the sensor to reduce the line to a spot).

PS. don't you have someone studying physics who can help you? They usually have optics in the curriculum I think.

PPS. this method might help at the cost of losing some light ... so you use one lens (system) to project onto a diffuser (with the rod/lenticular lens to make a dot) and then you use a separate lens to magnify the image on the diffuser for the sensor.

Patrick

Mon Nov 26 2012, 06:22PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Pinky's Brain wrote ...

You don't have a beam at the sensor, you have a defocused image.

Ah crap... i was afraid someone was going to say this...

if im all wrong on this matter, then i need someone to draw a simple pic, showing a conventional 0.25" wide CCD chip and a single lens and Focal point, becuase im not understanding any of your points, though im sure your all right...

i need an example relationship, like how a 640x480 pin hole camera works...

I know the XV-11 neato vacuum bot's lidar works with a single lens, ir filter, and panavision sensor, i just want to duplicate their optical train...

Pinky's Brain

Mon Nov 26 2012, 06:54PM

Registered Member #2901 Joined: Thu Jun 03 2010, 01:25PM
Location:
Posts: 837

Just going to run through the numbers because I know how to do them, but I don't have an intuitive grasp of what will come out.

Given the size you want to make the assembly the centre of the lens will probably be around 50 mm off side of the laser beam and we can use primary lens with a focal length of 25 mm. We are interested in the image at the focal plane, because that's what we need for an infinity focused system. With an object at 0.25 meter this gives a magnification of 0.025/0.25 = 1/10th, so the image will be a whole lot fatter than 4 um ... but you can determine the centre with some image processing.

The distance of the image for objects at 0.25m and 10m (by the way Patrick, stop using imperial already) from the origin of the laser can be determined by tracing a line from the object through the centre of the lens to the focal plane. X is distance from the lens, Y is distance on the focal plane.

tan(a)=0.05/X, Y=tan(a)*(X+0.025), Y=0.05*(X+0.025)/X
X = 0.25 => Y = 0.055
X = 10 => Y = 0.05

So a difference of 5mm ... huh, what do you know ... ballpark correct, I think if you increase focal length 2x you're there (do the numbers yourself).

In short : one setup which would work is 50 mm FL lens with it's centre 50 mm off the origin of the laser, with the sensor at the focal plane with one edge lined up with the centre of the lens and the other edge away from the laser (a lenticular or rod lens in front of the sensor with the sensor again at the focal point will get more light to it, but when I said that before I did not consider alignment ... which is rather critical, so you might want to skip it). Also try to get a laser with a thinner line, image processing can only do so much and it will improve SNR.

PS. of course there a whole lot more which would also work, but it's a vast multidimensional problem I'm not going to try to work out ...

2Spoons

Mon Nov 26 2012, 09:06PM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
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Posts: 615

I think you need to take a step back and work out what optical resolution you need at what distance, so that your ranging calculations give you the accuracy you require. Once you work out what your field of view needs to be you can work out the lens focal length from similar triangles. Don't worry about trying to match the laser line width to the pixel size - at infrared wavelengths there will be noticeable crosstalk between pixels, so the digital image will always be slightly fuzzy. THIS IS A GOOD THING - it allows you to interpolate across several pixels to get sub-pixel resolution of the laser line position.

I have used Panavision linear sensors at work, building infrared touchscreens, so I'm reasonably familiar with the issues you are encountering.

Pinky's Brain

Mon Nov 26 2012, 09:50PM

Registered Member #2901 Joined: Thu Jun 03 2010, 01:25PM
Location:
Posts: 837

Meh, it's not like he has a lot of room to make choices with a single lens ...

He gets to pick either focal length OR distance of the centre of the lens from the origin of the laser, that's it ... the moment you pick one everything else rolls out automatically, because an object (or rather the part of it illuminated by the laser) at ~0.25 meters has to be projected to one end of the sensor (at the focal plane, because of infinity focusing) and at infinity the other (well 45 feet, but that's essentially infinity here). The greater the distance from the origin the more linear the depth resolution is distributed across the sensor. So all he needs is to understand the thin lens equation and a decision how wide he wants to make the device.

BTW, Anchor Optics has a cylinder lens for 8.5$ which fits the sensor well, if you glue some glass under it with a total thickness of 11 mm you only have to position it in 2D, the alignment is still critical but in 2D probably doable ... should give quite a bit increase in received light.

Patrick

Tue Nov 27 2012, 03:14AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

i have parts on the way, and am willing to use cylinder optics too. my decisions are mainly meant to make the sensor optic easy to build/align/calibrate...

not sure what your guys' points are, still trying to learn/understand without pics. ill keep reading...im going to my physics professor tomarrow for this reason...

im hoping for the laser to be about 10-16um wide ( though im flexible on this requirement). Oops! there i go with that dam metric system agian.

PS, only communists and cowards use the metric system.

Shrad

Tue Nov 27 2012, 07:53AM

Registered Member #3215 Joined: Sun Sept 19 2010, 08:42PM
Location:
Posts: 780

you need to use separate optics

a small, neatly focused line for laser output (eventually with a beam pickoff of say 5% with a small piece of glass at 10Â° incidence), and a BIG objective lens with a high numerical aperture for grabbing most of the incoming light, and keep image focal at the average center of your sensor

if you use a pulse train, why bother the pixel size? wouldn't a reverse biased PIN photodiode suffice for an easily reproducible design?

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