Comments on Double Slit Experiment for Accurately measuring distances?

[kevin99]

I'm thinking about using two slits, a webcam and a laser to calculate distances for a project.

Usually you measure the distances between maxima but this can be easily measured in a dark room using Matlab and it's image processing routines.

I can create the slits and accurately measure them using an optical microscope.

Is this a good or bad idea? Using error analysis, I think I can get the distance down to 1 part in 1000 so 1mm over 1 m away or .5mm over 2m away.

Maybe I can combine it with a cheap interferometer and make it super accurate. Problem with an interferometer is that you can only measure within 1 wavelength.

Any comments?

 

[kevin99]

If you go to:

http://www.ub.es/javaoptics/applets/YoungEn.html

I would know the wavelength of light of my laser, the distance between the slits (optical microscope), distance between maxima (camera+matlab+image processing toolbox), therefore I can calculate the distance between the plates accurately?

 

[mgb_phys]

You have to account for the slits and screen not being parallel. If they titl as they move the spacing on each side of the maxima will change, easy to calculate out but might be a S/N problem.

For very small distance using something like Newton's rings and counting fringes is very common. It's easy to interpolate the position of a fringe centre to very high order with simple quadrature detectors.

 

[kevin99]

Actually I was going to mount it on an XY table and scan both X and Y directions so I can easily account for any tilt.

I'm trying to get it down to 1micron measurement so I can render a 3d surface.

I can engrave slits about .002 inches in thickness and separations in increments of .0001 inches with a CNC mill.

Are there any cheap supplies of highly coherent laser pointers?

What other sources of error are there that I should look at?

 

[mgb_phys]

the trouble with using fringes for this is that you need a finite size flat surface to act as the screen, so you can't easily measure fringe width on a highly curved surface.

There are some practical problems, firstl although the CNC mill has 1 thou increments it doesn't mean it can cut slits 1 thou apart. It's like your inkjet printer having 2000dpi, doesn't mean it can print object 0.5thou across.

Coherence of the laser isn't a problem - you are only looking at the central (white light) fringe. a bigger problem is wavelength stability which varies with temperature and mode hopping as laser light is scattered back into the diode.

For measuring the distance to a single point with high accuracy, I would look at a michelson interferometer - assuming the surface is reflective enough.
The single wavelength isn't a problem if you have a smoothly varying surface since you can keep track of how many times you have wrapped around a new wavelength. It is a problem if you have abrupt steps in the object.

The other solution is to vary the brightness of the beam in a sinusoidal pattern and compare the brightness of the returned and outgoing light. You know the speed of light, the frequency of the variation and so you can calculate time and distance from the phase difference - this is how the DIY red dot distance meters ( eg Leica Disto) work.

 

[kevin99]

I've tested the CNC and made some pcb traces that are 1 thou in thickness so don't see a problem making slits the same width.

Time of flight measurements are not very accurate with cheap electronics. Even high end are only good to a few mm over tens to hundreds of meters.

What I was thinking is if the object is against a wall, the fringes will tell me distance to the wall. If there is an object in the way, the fringes will be distorted and I can calculate from the separation the image separation.

Most 3d laser scanners work on triangulation of a few laser lines with a CCD.

I figure I can get better accuracy with sharp fringes from a double slit.

 

[mgb_phys]

Time of flight measurements are not very accurate with cheap electronics. Even high end are only good to a few mm over tens to hundreds of meters.

The brightness variation phase wants aren't time of flight. You are just comparing the relative brightness of outgoing and reflected light - and since you are doing this continually over many phases it can be very accurate. Cheap ones work at the mm level because of limitations in the laser and need to have a quick measurement.

What I was thinking is if the object is against a wall, the fringes will tell me distance to the wall. If there is an object in the way, the fringes will be distorted and I can calculate from the separation the image separation.

Are you talking about measuring distance form the fringe angle - or a structured light scheme where you project a grid or series of lines and look at changes in the shape?
This is good for complex curved surfaces.

Most 3d laser scanners work on triangulation of a few laser lines with a CCD.

Or multiple cameras looking at the same scene + strutured light.
For some amazingly accurate ones see Faro's products.

 

[kevin99]

Thanks for the helpful comments.

I'm thinking about structured light but the structured light comes from of a double slit.

That way a very linear grid can be made with double slit and I can scan it across the object to fill in the spaces.

On the cheap I can make the slit for next to nothing and a cheap laser pointer and webcam are also cheap.

The XY ball screw translation stage I picked up off ebay for $30 and added my own stepper motors.

 

[mgb_phys]

The main probelm with slits as structuredlight is that the brightness falls off quickly so you can only really use the middle few.
A cheap laser pointer will come with a little holographic line generator that might be better. The challenge is probably the reconstruction algorithms.

The other option if you are using lead screws and stepper is to make a sort of laser non-contact Atomic Force microscope!
Keep the slit fringes the same size on the object my moving the screws, you keep the distance laser-object fixed and read the position from the steppers.
Slow but simple.