# Imaging Fresnel Lens Theory

Hello All,

I am in need of an optics expert on imaging, and in particular a fresnel lens is being used as for an imaging device. From my understanding a condenser lens can be considered equivalent to a plano-convex lens.
Setup:
• A condenser fresnel lens is used, for which both the fresnel and plano conjugates are finite. Meaning these conjugates could be found using the thin lens equation. This only would apply if we wanted the light to focus to a point, which is not what we want.
• Light source projecting a pattern into the fresnel lens.
• Ideally the image produced should be similar to that of 25ft, when in actuality the source has only traveled approximately 3-4'.
• When comparing the pattern at the same distance without the lens, there is a clear difference.
• Image plane at the focal length, for which we should see a formed image.
• With initial testing, the size of the image stays the same no matter the light source location. The only thing that actually changes is the amount of the light source that is projected.
A few questions:
1. What is the object being imaged? (The object is not the light source but rather it's projection?)
1. How does this translate to the traditional thin lens formula?
2. The image looks best when the image plane is at the focal length. Why is this this case for imaging a light source?
3. Are there any articles/books that would be a good reference for imaging using fresnel lenses?
Any thoughts or suggestions will be very much appreciated!

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sophiecentaur
Gold Member
2020 Award
Summary:: Attempting to understand how a fresnel lens is used in an imaging scenario. Also fresnel lens theory in general, as well as answer a few of my questions.

This only would apply if we wanted the light to focus to a point
Afaik, the condenser system attempts to make sure that as much light as possible gets through the lens. In the days of a large area projector filament, an image of that filament was formed in the plane of the projector lens. The last thing you want is a sharp image of the filament to fall into the Object Plane. This, I think, is why a conventional condenser lens is so fat and very far from being a 'thin lens'. A fresnel lens can be much flatter and achieve the same end. The purpose of the illumination optics is not to produce a sharp image on the screen but to get as much light out as possible (hence the back reflector which produces an inverted image of the filament in the plane of the filament - to 'fill in the gaps' in the filament matrix. I think the task of the system for a halogen lamp is a bit easier as it is pretty small but the same thing applies.

Iirc the slide is placed at the focal plane of the condenser and the filament is placed to make its image in the plane of the projector lens.

The optics of projecting the slide onto the screen is a separate consideration, once the illumination has been taken care of.

tud623
Thanks for the response!

Is there a correct distance between the condenser system and projector system that will produce the sharpest image? Or just is the maximum amount of light the only consideration? As in the FOV would be about the size of the aperture of the projector lens system.

Also in particular I am only using a single element fresnel lens to condense the light. Why would changing the light source distance to the fresnel lens not change the light source shape? It rather cuts the field of view as you move away from the lens. I would also consider this to be a large diameter point source.

Drakkith
Staff Emeritus
My understanding is that a condenser lens is not usually used to form an image, but to bring a diverging cone of light into collimation or convergence (in other words, the light rays become parallel or converge) to illuminate an object. An imaging lens can do this too, but a condenser doesn't always have to be manufactured with the same tolerances as an imaging lens. Hence why fresnel lenses can be used even though they have severe optical aberrations.

I'm also a little confused about your setup. Are you using a projector? Or do you just have a condenser and a light source?

tud623
My understanding is that a condenser lens is not usually used to form an image, but to bring a diverging cone of light into collimation or convergence (in other words, the light rays become parallel or converge) to illuminate an object. An imaging lens can do this too, but a condenser doesn't always have to be manufactured with the same tolerances as an imaging lens. Hence why fresnel lenses can be used even though they have severe optical aberrations.

I'm also a little confused about your setup. Are you using a projector? Or do you just have a condenser and a light source?
Thanks for the response.

As far as setup goes there is only a condenser and a light source. There is no projector, I may have referred to a projector as a example because this produces light. In a effort to get a similar comparison to what I am trying to do. For a projector it seems you wouldn't want to image the filament on the wall, but I know this is much more complex than the system I am trying to setup.

hutchphd
Homework Helper
Your question is a little bit diffuse. What are you making?
In general a Fresnel lens can be thought of as a thin lens with a lot of aberrations. Fresnel thought it one of his best inventions, and anyone on the water can attest to it utility. Here is a good article:
https://en.wikipedia.org/wiki/Fresnel_lens#Imaging

sophiecentaur and tud623
Your question is a little bit diffuse. What are you making?
In general a Fresnel lens can be thought of as a thin lens with a lot of aberrations. Fresnel thought it one of his best inventions, and anyone on the water can attest to it utility. Here is a good article:
https://en.wikipedia.org/wiki/Fresnel_lens#Imaging
This is already a device that I am trying to reverse engineer the theory. As far as sharing what it is, the most I can say is this device is attempting to form the light source pattern onto an an image plane where it can be captured. In particular, the pattern formation must match closely to that on just a wall 20' away.

This system already does this, but I am trying to determine why and exactly how the pattern forms so well at the focal length. Part of the confusion is I may be using incorrect terminology regarding condenser and trying to do imaging with the fresnel lens. The quality is somewhat important but not really the main concern. With this single lens the quality is good for the application.

hutchphd
Homework Helper
Summary:: Attempting to understand how a fresnel lens is used in an imaging scenario. Also fresnel lens theory in general, as well as answer a few of my questions.

• This only would apply if we wanted the light to focus to a point, which is not what we want.
If you are trying to form an image you indeed do want to focus a point to a point for each element of the object/image. I always thought Sears and Zemansky did a nice job on intro optics.
Also in my vernacular a "condenser" lens is just a fat (ie short focus) plano convex lens often made of heat resistant glass. Its just a lens, so I don't understand the distinction. Maybe there are subtleties i don't understand.

If you are trying to form an image you indeed do want to focus a point to a point for each element of the object/image. I always thought Sears and Zemansky did a nice job on intro optics.
In I am thinking in a tradition thin lens optics sense, then I would agree with you. If I understand you correctly, I believe this would be true if we wanted to image the filament, but that isn't this the correct object we want to image. The biggest issue I have with my understanding is I am not sure what the object actually is in this particular setup. Is it still the filament, but the light just needs to be cutoff at the focal length, or would the object actually be the light when it hits the fresnel. We want to "image" the pattern that the filament produces. Imaging maybe is not the correct word I am using, and I am not sure exactly what word this would be.

There is something missing in my understanding, where we can't consider this to be a traditional optics scenario. I find this somewhat confusing as I know I am missing a few key points that are needed to understand this.

hutchphd
Homework Helper
Is there an aperture that forms the image? Can you look at the innards of the apparatus?

Is there an aperture that forms the image? Can you look at the innards of the apparatus?

Yes I have access into the full system and the inside. It is nothing more than an image plane at the focal length and the fresnel lens.
The size of the aperture is the size of the clear aperture of the fresnel lens.

hutchphd
Homework Helper
What do you mean by "image plane"? Where is the source of light?

What do you mean by "image plane"? Where is the source of light?
Just imagine a plate, which is larger than the aperture of the fresnel, that the formed light hits. This plane is located at the focal length.

hutchphd
Homework Helper
I think you need to draw the apparatus. This is getting silly.

Here is a general diagram of the apparatus. I apologize if I am not clearly explaining it.

I put the 'image plane' a bit off of the focal length so you could see F, but in reality they are at the same location.

Hopefully this can clear up some confusion.

hutchphd
Homework Helper
How do you identify the "image plane" in the apparatus???

How do you identify the "image plane" in the apparatus???
In terms of the naming, all I am referring to would be the place where the pattern forms for this particular system. In terms of material there is no transmission through the "image plane". If you had an open system for example, you could assume it is a white wall. This would be equivalent to the setup.

The apparatus ends right after this "image plane". It appears this may be a poor nomenclature as you could also consider a theoretical plane at Si as an 'image plane' as well. Refer back to the diagram for Si location. (The typical optics equation for object and image where magnification, locations of these dependent on the other, etc.)

Instead of image plane, lets just assume that a wall is there preventing the light from traveling any further. Would you agree that this is partly why my description is confusing?

hutchphd
Homework Helper
Summary:: Attempting to understand how a fresnel lens is used in an imaging scenario. Also fresnel lens theory in general, as well as answer a few of my questions.

ight source projecting a pattern into the fresnel lens.
• Ideally the image produced should be similar to that of 25ft, when in actuality the source has only traveled approximately 3-4'.
• When comparing the pattern at the same distance without the lens, there is a clear difference.

I'm sorry but I a have no idea what you are saying here. Is 25ft the Fresnel distance????
Can you not just say what you want to accomplish? The only possible image produced in this setup is the source (filament.....LED.....arc ??) or something behind it.

I'm sorry but I a have no idea what you are saying here. Is 25ft the Fresnel distance????
Can you not just say what you want to accomplish? The only possible image produced in this setup is the source (filament.....LED.....arc ??) or something behind it.

The purpose of system this is for the beam pattern to form at the "image plane".
Example:
• Lets say a halogen light is producing some pattern, which fully forms at 15 feet between the light source and the wall (no lens in between).
• Now the system setup:
• 24" from light source to fresnel.
• 24" from fresnel to wall. This also happens to be the focal length of the fresnel lens (24")
• 48" or 4 feet of total distance
• This system will form the same pattern as if the light source was actually 15 feet from the wall. Even though it has only traveled 4 feet. At 4 feet the light pattern would not normally be fully formed but an underdeveloped pattern.
• In this scenario, the halogen will not be imaged at the wall, but rather the projection of light that the LED will form.
• From a pattern perspective, it would not just be a blob of light. This would have a distinct shape, lets say a box pattern overlayed onto a line of light.

Lets just say this is the pattern that will be projected. It will require multiple sources oriented in different angles to achieve this pattern at a certain distance from target. This system would be expanding the light from the point it leaves the source.

hutchphd
Homework Helper
You lost me in the beginning. Why does the halogen light produce a pattern? The source is almost isotropic.

You lost me in the beginning. Why does the halogen light produce a pattern? The source is almost isotropic.
Possibly a reflector of some sort. I am trying to give you an example where a pattern is generated in some way. The problem is I am not an optical designer, clearly reflected in my knowledge in optical systems. Specifically I have no idea how the pattern is created, but a flashlight uses a reflector. But it may be possible to modify the reflector in such a way that it projects different parts of the light in different directions.

This is way outside of my wheelhouse in terms of pattern generation.

Drakkith
Staff Emeritus
I'm with hutchphd. Why and how does the source produce a pattern in the first place? Is there a simple mask placed just after the light, or is there some other lens integrated into the light source that helps produce the pattern?

I put the 'image plane' a bit off of the focal length so you could see F, but in reality they are at the same location.

And you're sure that is where the image plane is actually located? The only way that this should be true is if the incoming light is parallel, meaning that the source is either located near infinity or there is another optical element in the apparatus.

I'm with hutchphd. Why and how does the source produce a pattern in the first place? Is there a simple mask placed just after the light, or is there some other lens integrated into the light source that helps produce the pattern?

And you're sure that is where the image plane is actually located? The only way that this should be true is if the incoming light is parallel, meaning that the source is either located near infinity or there is another optical element in the apparatus.

If there is no angle to any of the light and there is just a mask, then of course it will always be a larger version of this at any further distance from the source.

This is just a theoretical pattern but one way I can think of is having three separate sources that produce three different parts of the pattern I provided. Lets say three separate LED's are making 3 rectangles, and are in an orientation where at a target distance will be at specific points, and at specific sizes. Maybe one of them you want to be stretched out more so it must be at a specific angle as well.

Of course several lenses could also be used on the light source along with masking of a specific LED. Does this seem feasible?

Lets go back to the the 15' and say that's the target distance. The pattern desired is at this distance, and in my mind an optics engineer reverse engineers the pattern from there probably with software.

From the information I have been given, the image plane is definitely at the focal length. As well as the fresnel information that I have is direct from supplier is given. I can also confirm that there are no other optical elements inside the aparatus.

What you are saying makes sense, but let me ask you this. Wouldn't this be true if the image was supposed to be of the flashlight reflector itself instead of the produced pattern? Like exact size and shape of the reflector?

Wouldn't it make more sense that we are cutting off the projection of this light off at a certain point?
The only thing is the fresnel lens somehow forms the pattern much faster in 4 feet rather than the 15 feet needed normally to form.

This reasoning behind this faster formation is the key bit of information I am after.

Drakkith
Staff Emeritus
This is just a theoretical pattern but one way I can think of is having three separate sources that produce three different parts of the pattern I provided. Lets say three separate LED's are making 3 rectangles, and are in an orientation where at a target distance will be at specific points, and at specific sizes. Maybe one of them you want to be stretched out more so it must be at a specific angle as well.

Again, how are they making the pattern? LED's don't form rectangular patterns by themselves.

From the information I have been given, the image plane is definitely at the focal length.

Which information are you referring too?

What you are saying makes sense, but let me ask you this. Wouldn't this be true if the image was supposed to be of the flashlight reflector itself instead of the produced pattern? Like exact size and shape of the reflector?

Wouldn't what be true? The reflector is at a slightly different distance than the light source, that's about the only difference between the two.

Wouldn't it make more sense that we are cutting off the projection of this light off at a certain point?
The only thing is the fresnel lens somehow forms the pattern much faster in 4 feet rather than 15 feet.

I'm not sure. I still don't fully understand the setup unfortunately.

sophiecentaur
Gold Member
2020 Award
(in other words, the light rays become parallel or converge
The condenser lens has a very short focal length and it needs to be as wide as possible to get as much light from the bulb (that's a very low f number). Making it planoconvex is a way to achieve this without having the condenser very close to the bulb probably.

Also in my vernacular a "condenser" lens is just a fat (ie short focus) plano convex lens often made of heat resistant glass. Its just a lens, so I don't understand the distinction
Yes - I agree that the name 'condenser' classifies it as good for that job and probably a rubbish lens for anything else.

In I am thinking in a tradition thin lens optics sense,
I don't think there's any chance of that for a lens of that sort of diameter and focal length.

Lets say a halogen light is producing some pattern, which fully forms at 15 feet between the light source and the wall (no lens in between).
I don't know why that would be what happens in a regular projector or just with the filament and spherical reflector.

The focal length of the condenser will be short (for that f number) and cannot be allowed to produce any recognisable image where the slide image can sit, in front of the projector. If the focal plane of the condenser lens is chosen to be in the plane of the slide then the condenser will produce a spatial Fourier transform of the image (filament) in that plane and a low quality image of the filament will be formed according to the formula 1/f =1/u + 1/v, somewhere close, out in front. The FT will be very diffuse and uniform all over the slide, which is just what you want.
But you are not clear about what you are 'trying to do'.

hutchphd