Compact Fresnel reflector or diffractive grating?

[nikosb]

TL;DR Summary

Can a modified diffractive grating act as compact fresnel refelctor?

Hi,

I have an imaging application, where a mirror with dimensions of 120x80mm at an angle of approximately 50 degrees to the mounting surface reflects a real image at approximately 11 degrees angle of incidence. Due to space limitations I need to reduce the height of the mirror. I was thinking of using a fresnel compact reflector as illustrated below :

I looked for fresnel compact reflectors, but they are typically used in large solar reflectors, and I couldn't find anything for sale. The only thing that resembles the fresnel compact reflector is a ruled/echelle reflective grating. My understanding is that ruled reflective gratings don't produce specular reflection, they refract light, and that refraction occurs when the groove spacing in comparable to wavelength. Could a modified ruled/echelle reflective grating, with groove spacing larger than the wavelength at the end of visible spectrum, i.e. 50lines/mm or less, be used to act as a fresnel compact reflector?

 

[sophiecentaur]

A fresnel element is an approximation to a simple reflector or refractor. There will be some diffraction at the fresnel steps. That (along with the masking effect of the ‘reverse slopes’ is why it’s not high quality.
But a diffraction grating works because of diffraction / interference and the grating is plane. There are thousands of lines in a diffraction grating whereas the active sections of the fresnel will each have just one (imperfect) ‘line’. The directions of diffraction maxima will not be the same as reflections because of the dispersion (which is the purpose of a DG.)

So the two don’t have a lot in common. Imo. But it would depend on the spectral width of your source.

 

[nikosb]

A fresnel element is an approximation to a simple reflector or refractor. There will be some diffraction at the fresnel steps. That (along with the masking effect of the ‘reverse slopes’ is why it’s not high quality.
But a diffraction grating works because of diffraction / interference and the grating is plane. There are thousands of lines in a diffraction grating whereas the active sections of the fresnel will each have just one (imperfect) ‘line’. The directions of diffraction maxima will not be the same as reflections because of the dispersion (which is the purpose of a DG.)

So the two don’t have a lot in common. Imo. But it would depend on the spectral width of your source.

Thank you for the reply. My background is not in optics so if I understand correctly what you explained is that a compact fresnel reflector will have specular reflection at each section except at the edges/steps where the light will diffract, correct?

I found this video on this company's website showing ruled reflective gratings (possible concave)

https://www.alibaba.com/product-det...offerlist.normal_offer.d_title.60396337At1OmU

While one can observe the refraction during most of the video, at second 7 it appears there is specular reflection of the ceiling. The reflected image doesn't look that bad either. I include a snapshot I took:

I agree that they two optical elements don't have a lot in common as one relies on the principle of refraction and the other on the principle of reflection. But I am trying to figure out if a compact fresnel reflector can be manufactured with the same technique as a diffraction grating, but instead of making thousand of lines per mm, increase the groove spacing to minimize/eliminate refraction and allow specular reflection, for example hundreds or tens of lines per mm? For instance, would a ruled/echelle grating designed for the infrared wavelength work as a compact fresnel reflector for the visible spectrum? If yes, how do I go about calculating the minimum groove spacing for a given reflection angle (i.e. 50 degrees) for the visible spectrum?

 

[sophiecentaur]

one relies on the principle of refraction

Diffraction!! It's important to get this right.
That alibaba thing works by diffraction. The fact that it disperses the light it reflects tells you that. Afaics, it's a 'fun' thing.
You state that you have an " an imaging application". What is it? What do you need this 'reflector' to achieve.

TL;DR Summary: Can a modified diffractive grating act as compact fresnel refelctor?

where a mirror with dimensions of 120x80mm at an angle of approximately 50 degrees to the mounting surface reflects a real image

A plane reflector produces a virtual image (let's get that right too). The angle of the reflecting faces is specifically chosen so that the reverse surfaces do not get in the way.

My background is not in optics

Fair enough but you need to get some basics, rather than relying on the old question and answer technique to get a solution to your problem. So far you haven't actually asked an answerable question. Those red arrows, labelled "reflected image" and " real image" mean nothing. An image is where the light ends up or appears to come from.
What you need is a basic school optics book (or a chapter in a Physics book. This is not a five minute job.