Have you ever wondered if there is an optics system that can translate an object to an image by a constant amount? This article will provide you with a detailed overview of this topic and answer any questions you may have.
The Problem
For a certain application, there is a need for an optics system where any incoming ray can be translated by a distance d along the optical axis, while remaining parallel to the incoming ray.
Additionally, the system needs to be shorter than d for the application. Such a system would image any point to a point shifted by d along the optical axis.
The question here is whether there is a name for such an optical system, if it is being used somewhere, how it would look like and where it is available.
The Solution
One possible solution to this problem is to use a grin lens with pitch 1.0. This system would have the desired property of translating the incoming ray by a constant distance along the optical axis. However, this system would be as long as d, which makes it infeasible for the application.
Another possible solution is to use multiple thin lenses. Specifically, four lenses with focal length f=d/8 or three lenses with focal lengths f, f/2, f in this order can be used.
In either case, two consecutive lenses are placed 2f apart from each other. However, it’s unknown if such a design can be made with small aberrations.
The Design
A real design for an optics system that translates an object to an image by a constant amount can be achieved by using the aforementioned four-lens or three-lens setup.
The four-lens setup consists of four lenses with focal length f=d/8, and two consecutive lenses are placed 2f apart from each other. The incoming ray is first refracted by lens 1, then by lens 3, and finally by lens 4. The image is formed by ray tracing from the exit pupil of lens 4.
The three-lens setup consists of three lenses with focal lengths f, f/2, f in this order, and two consecutive lenses are placed 2f apart from each other. The incoming ray is first refracted by lens 1, then by lens 2, and finally by lens 3. The image is formed by ray tracing from the exit pupil of lens 3.
In conclusion, an optics system that translates an object to an image by a constant amount can be achieved by using a grin lens with pitch 1.0 or a multiple thin lens setup. While there is no specific name for such a system, the design is feasible in real-world applications.
By implementing a four-lens or three-lens setup, one can construct such an optics system. However, it is important to ensure that the system has small aberrations to avoid any distortions in the final image.
Optics That Translates Object to Image By a Constant Amount
Have you ever wondered if there is an optics system that can translate an object to an image by a constant amount? This article will provide you with a detailed overview of this topic and answer any questions you may have.
The Problem
For a certain application, there is a need for an optics system where any incoming ray can be translated by a distance
dalong the optical axis, while remaining parallel to the incoming ray.Additionally, the system needs to be shorter than
dfor the application. Such a system would image any point to a point shifted bydalong the optical axis.The question here is whether there is a name for such an optical system, if it is being used somewhere, how it would look like and where it is available.
The Solution
One possible solution to this problem is to use a grin lens with pitch 1.0. This system would have the desired property of translating the incoming ray by a constant distance along the optical axis. However, this system would be as long as
d, which makes it infeasible for the application.Another possible solution is to use multiple thin lenses. Specifically, four lenses with focal length
f=d/8or three lenses with focal lengthsf,f/2,fin this order can be used.In either case, two consecutive lenses are placed
2fapart from each other. However, it’s unknown if such a design can be made with small aberrations.The Design
A real design for an optics system that translates an object to an image by a constant amount can be achieved by using the aforementioned four-lens or three-lens setup.
The four-lens setup consists of four lenses with focal length
f=d/8, and two consecutive lenses are placed2fapart from each other. The incoming ray is first refracted by lens 1, then by lens 3, and finally by lens 4. The image is formed by ray tracing from the exit pupil of lens 4.The three-lens setup consists of three lenses with focal lengths
f,f/2,fin this order, and two consecutive lenses are placed2fapart from each other. The incoming ray is first refracted by lens 1, then by lens 2, and finally by lens 3. The image is formed by ray tracing from the exit pupil of lens 3.Conclusion
In conclusion, an optics system that translates an object to an image by a constant amount can be achieved by using a grin lens with pitch 1.0 or a multiple thin lens setup. While there is no specific name for such a system, the design is feasible in real-world applications.
By implementing a four-lens or three-lens setup, one can construct such an optics system. However, it is important to ensure that the system has small aberrations to avoid any distortions in the final image.