What are the key considerations for imaging with a condenser fresnel lens?

[hutchphd]

The pattern from such a holograph is very sharp lines of nodes (diffracted) forward in an expanding square grid pattern from the laser spot. These then behave exactly like the "rays" in a ray trace which is I believe is what is being seen...just geometrical optics from there on so they become parallel by the lens. (?)

 

[tud623]

I don't understand this. You want a "good formed pattern" but a fresnel lens (or even a glass lens classed as a condenser) will not give you an image that's free of aberrations. So what does 'good'mean in your context?

You are correct that good is subjective and I did not really explain what I consider to be good. Abberations are not really that much of a concern for this setup, so the image can be somewhat poor quality both in sharpness and color. This pattern really forms at a distance 4 times longer than the setup with the fresnel. As long as this pattern matches between the two setups, then this is 'good'. The two setups being: light source to wall ~ 15', light source to fresnel to wall ~ 4'.

The 1/f = 1/u + 1/v formula requires the object distance to be known. The object distance for a laser beam is effectively a long way behind the laser (- ∞) if it's not followed by a lens or other element . If the plane of the focussed image is about F from the lens that would confirm where the 'Virtual Object' lies (All phases relate to the position virtual source of the laser). In your diagram, you label a "light source". Is that the hologram slide? The source is not actually at the hologram if you define 'source' as the place where all paths from a particular point are co-phased. This could account for your confusion.
What does your grid pattern look like at different distances, without the fresnel. Does it get bigger with distance, as if the source is located on your 'hologram' slide?

Did you ever consider using a 'real' object as a light source - like a bulb filament? Try that and get a better idea of the optics.

So you are saying any light source that isn't followed by another lens or element, then it is effectively at infinity? What if the pattern is produced with several optical elements before a pattern will actually be produced?

I would not consider the light source to be a hologram slide, because I am not exactly sure what you mean by this. It is a laser with another lens that press fits onto it, where this optical element creates a pattern (maybe this is a hologram by definition?)

The light source location is where the laser, or normally this beam pattern is created. The source is located directly at this location with any other optical systems after this. Yes the laser pattern always gets larger as you move away from the wall for example.

That is a good idea and I will try this.

Another side note that I thought of:
With the viewing plane at the focal length, isn't this setup very similar to a camera lens system? From my research it looks like the camera sensor is normally at the focal length of the lens. This beam has a very high intensity, and much of the surroundings will not be seen on this viewing plane. Similarly if you looked at a white wall there is not a reflection of everything in the room, as it is not intense enough to show that. A camera however is sensitive to very low intensities and will view everything in the room.
Not exactly the same setup but similar as we care more about the projection of light rather than looking at the environment and the light source.

This setup is very specific for looking at light with high intensity, as well as formation of the beam pattern.

 

[sophiecentaur]

The pattern from such a holograph is very sharp lines of nodes (diffracted) forward in an expanding square grid pattern from the laser spot. These then behave exactly like the "rays" in a ray trace which is I believe is what is being seen...just geometrical optics from there on so they become parallel by the lens. (?)

I think you are being over-simplistic about this process. Take a real object and the rays from a point spread out, as you say, but if you hold a frosted glass screen in front of that object, you will not see that object in the plane of the screen. This is different from a simple interference pattern which will appear the same on a screen - just bigger as you increase the distance. This is the situation with the hologram so your ray tracing doesn't describe it. Because the hologram has a larger aperture compared with the two simple slits, the pattern has sharper detail.
Introducing the hologram into the experiment completely changes things, just as it would in many other optical experiments.

Note, there are many holograms that produce an image that locates at single place in 3D space and it doesn't 'expand' in the way you describe. This is in contrast with the pattern of very sharp lines from a diffraction grating. It just isn't as straightforward as you are implying so one has to be careful. Hence my suggestion of using a conventional image to start with.

 

[sophiecentaur]

So you are saying any light source that isn't followed by another lens or element, then it is effectively at infinity?

That comment of mine was about a Laser Beam, which can be regarded as the result of many reflections between front and back half silvered mirrors - an 'infinity mirror' with a very distant object right at the end of the tunnel. That is the image that acts as the object when you use a laser. You can pass the beam through a lens and that can modify the position of the 'source' from behind the laser (a concave lens) or in front of the laser (a convex lens).

It is a laser with another lens that press fits onto it, where this optical element creates a pattern (maybe this is a hologram by definition?)

You really are drip-feeding us information aren't you? I know what you mean now. The "lens' you describe is not a lens; it's a hologram. I have a laser with a range of 'filters' you can put on it and project a range of holographic patterns on the wall. I would definitely class those filters as holograms. The image distance is wherever the wall happens to be. Where does this all fit into the diagram you posted?
If it really is like you say, then the position of the light source is, indeed, at -∞ and, no surprise, it appears bang in the focal plane of your fresnel (1/f = 1/v + 1/∞) and takes the form of your grid pattern. That's what you saw. Like I was saying to @hutchphd , introducing the holograph from the start is adding far too much complexity.

Another side note that I thought of:
With the viewing plane at the focal length, isn't this setup very similar to a camera lens system? From my research it looks like the camera sensor is normally at the focal length of the lens.

Yes. This is basic for a relatively distant object. But we are not dealing with a normal object here. Please try to think in terms of conventional object and image first and then try to take on board the nature of holograms. Those things are really new and not intuitive objects. You ever to think 'inside out' to get a grasp of them. Alternatively follow the Maths from the beginning. But I guess you want to avoid that if possible. (Fair enough)

 

[hutchphd]

I think you are being over-simplistic about this process. Take a real object and the rays from a point spread out, as you say, but if you hold a frosted glass screen in front of that object, you will not see that object in the plane of the screen.

Perhaps I am not being clear. The "hologram" in my supposition is just a 2D rectilinear diffraction grating (produced holographically I am certain) . The far field (>1cm) forward output from this gating when illuminated by laser is a series of diffracted "beams" that will have radial direction and ~rectilinear symmetry when interrupted by a plane surface. The lens simply changes the divergent beams from its focus to parallel beams. Intercepting these at any point downstream of the lens will produce roughly the same rectilinear pattern of dots, no longer divergent in size.
I guess I should say I believe you are overcomplicating this!

 

[tud623]

You really are drip-feeding us information aren't you? I know what you mean now. The "lens' you describe is not a lens; it's a hologram. I have a laser with a range of 'filters' you can put on it and project a range of holographic patterns on the wall. I would definitely class those filters as holograms. The image distance is wherever the wall happens to be. Where does this all fit into the diagram you posted?
If it really is like you say, then the position of the light source is, indeed, at -∞ and, no surprise, it appears bang in the focal plane of your fresnel (1/f = 1/v + 1/∞) and takes the form of your grid pattern. That's what you saw. Like I was saying to @hutchphd , introducing the holograph from the start is adding far too much complexity.

Honestly, this really wasn't my intention to drip-feed you, especially with this laser setup as it is more experimental testing and relevant to the theory more than the use of the apparatus. I have come to realize that describing optical systems it seems is rather difficult, if you don't understand the systems completely as well as don't understand the important details to share. So I apologize for my ignorance in that regard.

Is this laser experiment directly related to the use of the apparatus? Shouldn't this tell us something about how this beam pattern is directly forming at the focal length?

After all we know for certain that this forms correctly at the focal length. And we also know that the laser pattern doesn't change with distance to the fresnel. In my mind this confirms that the apparatus is setup correctly, but can we make the assumption that these light sources are coming from infinity as well?

 

[hutchphd]

Even assuming I understand the result of the laser beam experiment, I still have no idea what your (the OP) actual question is...what are we doing?

 

[tud623]

Perhaps I am not being clear. The "hologram" in my supposition is just a 2D rectilinear diffraction grating (produced holographically I am certain) . The far field (>1cm) forward output from this gating when illuminated by laser is a series of diffracted "beams" that will have radial direction and ~rectilinear symmetry when interrupted by a plane surface. The lens simply changes the divergent beams from its focus to parallel beams. Intercepting these at any point downstream of the lens will produce roughly the same rectilinear pattern of dots, no longer divergent in size.
I guess I should say I believe you are overcomplicating this!

I am following your logic here and understand the thought process.

If the divergent beams were changed to parallel beams wouldn't this mean the size would change on the viewing plane, as you get further or closer to the fresnel?

Instead even if the laser pattern is an a half an inch in size when it hits the fresnel it still becomes 4" on the viewing plane. Comparatively if the matrix is 8" when it hits the fresnel, then it becomes 4" on the viewing plane. If the rays truly became parallel, wouldn't this mean that the size of the matrix on the fresnel lens, is the size that is projected onto the image plane?

The thoughts you are proposing is exactly what made me believe that the size on the fresnel would just be projected to the viewing plane. Instead of being parallel, the rays seem to condense or expand to a specific size at the focal length, relative to where the light source is placed from the fresnel lens.

What determines this 'size' that is seen on the viewing plane?

 

[hutchphd]

In this example for the grating ~at the focus) just the size of the lens. This is not the same as forming an image in the usual way.

 

[tud623]

In this example for the grating ~at the focus) just the size of the lens. This is not the same as forming an image in the usual way.

I would agree that this isn't the usual way of image formation. This is very much the reason this is confusing for me, even seeing this entire system right in front of me.

In terms of the example I described, what exactly is this setup doing? What is expected to happen in this setup? What should be actually seen at the focus?What is the purpose of this apparatus?
A device that accepts in a light source (multiple point sources) and projects this light onto a viewing plane. Where the viewing plane, does not have an image of the light source system that emits the light (going back to the laser, the actual laser diode). Rather takes this multiple point source light source, and projects it in a way that forms the pattern smaller (only approximately 20" in size).

For a comparison the pattern really would be around 3-4 times wider/taller than that without the lens. Along with the size becoming smaller in comparison, it also "forms" the light in a way that the source looks as if it was 12 feet away from a wall.

I am trying my best to describe the purpose of this apparatus. Does any of this make sense?

 

[tud623]

Recently found a source that had this to say about the back focal length of a lens:
"Many important images and objects are located at the objective’s back focal
plane: the Fraunhofer diffraction plane, the Fourier transform of the image, the image of
the filament, and the image of the aperture iris. The phase plate of phase contrast and the
Wollaston prism of differential interference contrast are placed in the objective’s back
focal plane."

Do any of these explain what we are seeing? What is the Fourier transform of the image?

 

[tud623]

Recently found a source that had this to say about the back focal length of a lens:
"Many important images and objects are located at the objective’s back focal
plane: the Fraunhofer diffraction plane, the Fourier transform of the image, the image of
the filament, and the image of the aperture iris. The phase plate of phase contrast and the
Wollaston prism of differential interference contrast are placed in the objective’s back
focal plane."

Do any of these explain what we are seeing? What is the Fourier transform of the image?

Recently ordered a few optics books that have yet to arrive. I ordered the following:
'Optics' Eugene Hecht
'Modern Optical Engineering' Warren J. Smith

Does anyone recommend any other sources?
My only experience in Optics before this is a few college physics courses required for most engineers to take.

 

[sophiecentaur]

In my mind this confirms that the apparatus is setup correctly,

On what basis can you say that? You have not stated what it is supposed to do (at least not in normal terms used in optics) so how can it be - or not be working properly?

What is the purpose of this apparatus?
A device that accepts in a light source (multiple point sources) and projects this light onto a viewing plane. Where the viewing plane, does not have an image of the light source system that emits the light (going back to the laser, the actual laser diode). Rather takes this multiple point source light source, and projects it in a way that forms the pattern smaller (only approximately 20" in size).

But you are not dealing with multiple "point sources" You are dealing with a diffraction pattern. If the sources were points then the image would not behave the way it does. If you read what I have written about your diagram then you can see that the light source is effectively at infinity. Do you not accept that? How else can an image be formed at F? You have confirmed this so we have to take that as evidence.

It is very frustrating that you are not using the expected terms and your comments just don't seem to make sense.

it also "forms" the light in a way that the source looks as if it was 12 feet away from a wall.

Whatever can this mean? Are you saying that there is a virtual image and that you have a method of measuring where it sits? Or can you say you have produced a 'best' focus of a blurry image that's 12 ft away?

Does anyone recommend any other sources?

I seriously recommend an introductory book into optics so that you can get all your basics sorted out, like what a point source is, how a basic thin lens works and the basics of a fresnel lens. After all, a fresnel lens is only a low cost, low mass way of producing a low quality version of what a conventional lens can do a lot better.

Recently found a source that had this to say about the back focal length of a lens:
"Many important images and objects are located at the objective’s back focal
plane: the Fraunhofer diffraction plane, the Fourier transform of the image, the image of
the filament, and the image of the aperture iris. The phase plate of phase contrast and the
Wollaston prism of differential interference contrast are placed in the objective’s back
focal plane."

Do any of these explain what we are seeing? What is the Fourier transform of the image?

I already mentioned the FT issue. Each of the concepts mentioned in that post require some detailed study and understanding before it's worth bringing them up. As they stand, it's just Word Salad.

I guess I should say I believe you are overcomplicating this!

Except that you don't seem to acknowledge the difference between an array of point sources and a diffraction that 'looks like' an array of bright rays. Once those dots have been formed on a screen then the coherence goes and they become point sources but not until. The OP doesn't mention any form of screen which could do that. Unless there is something at his "image plane or F" plane that's on his diagram. But anything after that would be diffuse and no image would be formed at all.

I am getting fed up with this thread as it's going nowhere. Apart from the diagram, the rest means very little to me; it's in a different world from the Optics I learned.

@tud623 perhaps you could re-read the (second) post of @Drakkith which re-states the situation in another way that may make sense to you.

 

[Drakkith]

@tud623 I'm with Sophie here. Your source is something that goes beyond simple geometric optics and you should ignore it for now until you understand more about how 'conventional' sources and optics behave.

 

[hutchphd]

Once those dots have been formed on a screen then the coherence goes and they become point sources but not until

What screen? I made no mention of a screen. One more try...If one were to put a little "smoke" in the air, one would see diverging "laser" beams radially emerging forward from the 2D grating. Those intercepted by the lens would be bent to make a bundle of parallel beams. Just like tracing rays...just that simple. No coherence issues involved.
I wholeheartedly concur with your advice that the OP needs to learn some optics. I am a little frustrated here also.

 

[Tom.G]

If one were to put a little "smoke" in the air,

That reminds me of an old joke that sort of strikes home here.

Three optical engineers were in the lab one day where a technician had just completed a prototype.

The engineers were arguing about the light path and location of focal points in the apparatus, each had a different idea of what was going on.

The technician, after listening to this for a while, decided he was fed up with the discussion. He light up a cigarette, blew some smoke into the light path, and walked away.

Cheers,
Tom

 

[sophiecentaur]

What screen? I made no mention of a screen.

I know you didn't but it's the only way you will get your 'point sources' that are not at minus infinity from the laser sourced beams he's talking about. Where would you find point sources along those beams until they hit something? In smoke, of course you will see many point sources but each smoke particle (tiny screen) takes some light from the beam. If you focus the beams to a point then that is a point image but where is that in this setup?

If you are correct then how is his Image focus at an image plane that is at F? F is where an object at infinity is focussed and not where his light source is in the diagram? If I have got it wrong then can you help me by explaining that away? Because of the coherence, each of the beams from his coherent source has a source that's the same as the laser's. (Near enough)

If you look at a laser beam it doesn't spread out as if from a point at the end of the laser. The beam will be parallel (as we know) and not a wide cone, which it would be from a point on the exit. The spread of the beam from a laser depends on the effective number of reflections within the laser and the physical length. One short tube becomes a much longer tube and a narrower beam. (As in my idea of an infinity mirror.)

PS the gizmo on the end of the laser is not a diverging lens.

 

[hutchphd]

If you look at a laser beam it doesn't spread out as if from a point at the end of the laser. The beam will be parallel (as we know) and not a wide cone, which it would be from a point on the exit.

Laser beam through diffraction grating:

Do you now understand what I am talking about? I am happy to discuss.

 

[sophiecentaur]

Do you now understand what I am talking about? I am happy to discuss.

I'm happy too; it is sorting out my mind usefully.
Yes. We both see the same thing but I think your interpretation is 'not right' or perhaps 'limited'. Looking closer, you can see that there is dispersion which forms, say four separate orders (just looking at a single colour).

Imagine that the grating (representing what the OP has) behind a screen so that all you can examine is those beams. They all emanate from, apparently, a single location - the grating. However, a close up of one beam will show a beam with parallel sides (same angle all the way along - ignore the diffraction due to the limited aperture). If you had to use that beam to estimate where the source is, you would say that it's at 'infinity'. So you would have conflicting observations; beams spreading out from a nearby 'point' but single beams with apparent sources at infinity. You are seeing one thing and I am seeing another.

Now replace the grating with a box with a halogen bulb plus simple filter and an array of holes in it and look at one of those mimic beams. The beam will be diverging as if from a source that's inside the box; that's conventional non-coherent optics. You could definitely say that the source is a point. No conflict here and we will both interpret it in the same (conventional) way.

If you use a convergent lens on both of those bundles of light, you will get different results. The individual split laser beams will form sharp spots at F and there will be a scaled image, consisting of defocussed spots, formed in the plane at v according to the f and the u.
For the halogen bulb arrangement, you will get a sharp image of the array of holes at v. Point sources to point images.

There are a couple of caveats, concerning the information we have been supplied with. Was the "Image Plane" described in the diagram, actually identified? Probably the least worst result of focussing using the fresnel. My reasoning is based on a good lens and it fits with what has been reported. It could be that all that's being seen is due to the aberrations of the fresnel lens so a good conventional lens should be used as a reference.

However, the whole situation as described is, itself, very defocussed and the description (including that strange diagram of the odd shaped figure) is in very unfamiliar terms.

Cheers

 

[hutchphd]

Very clear explanation...much appreciated. I think I still disagree with the following (color enhanced):

Iimagine that the grating (representing what the OP has) behind a screen so that all you can examine is those beams. They all emanate from, apparently, a single location - the grating. However, a close up of one beam will show a beam with parallel sides (same angle all the way along - ignore the diffraction due to the limited aperture). If you had to use that beam to estimate where the source is, you would say that it's at 'infinity'.

Thus is multi-slit diffraction and the beams have a small fixed angular width in the far field. This follows from the finite wavelength width of the laser...think about the color pattern produced by white light: it gets bigger with distance from grating. So with the grating a little outside focal point the lens makes this a little better. But you are thinking about a spectrometer with the "slit" effectively at infinity and you are indeed correct. But it really doesn't matter here.
What is hanging you up is essentially depth of field. If I shoot a laser beam through a lens it does indeed converge at the focus and then diverge...but by how much? The effective aperture of the lens for this circumstance is the size of the laser spot on the lens ! Maybe 1mm. So if f=10cm then the beam diverges 1/100 radians. So even for a fat lens the depth of field extends effectively to infinity.
I suggest the following experiment which requires a laser pointer and fat lens (I used my shop magnifier light) and a white card. Grab said items and play. I thought my analysis correct but found it a very useful 10 minute nonetheless.
All the beams will stay beams for our practical purposes.

 

[sophiecentaur]

Thus is multi-slit diffraction and the beams have a small fixed angular width in the far field. This follows from the finite wavelength width of the laser...

. . . which is what I already said when I drew a distinction between the laser and conventional rays. Conventional rays diverge in an obvious and finite way from where they are formed.

All the beams will stay beams for our practical purposes.

Yes I agree and their origins are at infinity and not at the plane of the grating. If, instead of a grating, you used a mirror to produce a single output beam, would you say that the Source Image position is in the plane of the mirror? Of course not. So why say that the image in this case is at the grating? The beams all converge on the grating but are you saying there is no difference between that and my theoretical filament lamp in a box of holes?
I guess my problem is only when the source position is needed or specified. And that applies here if we are discussing the 'Image Plane" in the diagram at the top of the thread. Where would a source have to be in order to be focussed at the Image Plane?

The depth of focus point you make has made me think and it's definitely relevant. But what is the OP talking about when he describes an Image being focussed at F? Perhaps what is being described is suffering from a poor laser source (a lot bigger than 1mm) and an obviously poor quality lens 'substitute'.

I have a slight glimmer about this. It is true to say that an observer moving from side to side would identify the direction of the source (when his eye was intercepting one of the beam) and that would lead him to deduce that the source was in fact at the grating (as long as the spread of the beams was not detectable). If the lack of spread was detectable then there would be a conflict. I have sort of said this already but, as you imply, it's all a matter of the actual numbers involved. There is a subtle difference between the coherent and non coherent cases but I think I can now accept that it could be OK to treat the grating as a source - for most purposes.

 

[hutchphd]

Of course not. So why say that the image in this case is at the grating? The beams all converge on the grating but are you saying there is no difference between that and my theoretical filament lamp in a box of holes?

The filament lamp in a box of holes would be the same if the filament had zero size and the holes had no diffraction limits so that you generated good beams.

I guess my problem is only when the source position is needed or specified. And that applies here if we are discussing the 'Image Plane" in the diagram at the top of the thread. Where would a source have to be in order to be focussed at the Image Plane?

This is why I am discussing depth of field. To focus the individual beams (dots) is easy: the depth of field is very deep because the effective lens aperture is tiny for each beam. For the size of the dot pattern to remain independent of image distance, however, the source position must be near the "front" focus, because it requires the whole lens to produce the pattern (the geometry is obvious I think).

 

[sophiecentaur]

The filament lamp in a box of holes would be the same if the filament had zero size and the holes had no diffraction limits so that you generated good beams.

That's not actually true. The beams from holes in a box diverge from the point at the centre. (Angle proportional to d with filament at d=0, even for "good beams") The beams from a diffraction grating diverge only due to diffraction limiting by the grating aperture and the angular spread is much less so the virtual source position is way behind the grating. That is particularly obvious for a monochromatic source in both cases.

But I'd love to know what actual image is produced in the 'image plane' that's in the diagram. I can't even a hazard a guess.

 

[hutchphd]

Yes the holes would also have to be zero size (which presents both diffraction and intensity issues!)...the hologram is really a good idea for this
As I said each of the beams will pretty much remain a beam for a long distance behind (because of "depth of field for each beam" ). Since these beams come ~from the focus they will emerge paraxially behind the lens and if the holographic grating has square symmetry and appropriate "blaze" there will be a square array of beams paraxially out to infinity...(or at least far enough, the beams will very slowly get fatter).
I had forgotten how nicely this all works out and had fun playing with my big lens and violet laser pointer (said pointer having cost 6 bucks: it would have been priceless when I started this stuff). The joys of the optical bench.