Computer Vision (26) and Optics

Here's another set of images that demonstrate this crisscross nature of light cones. Here I placed the matchstick at the corner and blocked any chances of light crossing the stick and reaching the aperture of the lens. You can easily find the difference between the first and the third images. The missing sector of the circle has moved to the other side, from left top to bottom right.

Computer Vision (25) and Optics

The light cone that I was describing till now will be observed when the actual focus point of the object lies beyond the sensor, i.e. the light rays from the object have still not converged when the plane of the sensor was encountered.

After the focus point is reached the rays crisscross and start diverging once again. Again this crisscrossing can be captured on the sensor by moving the focus point beyond the object.

The sequence of images below were taken by moving the focus point behind the object of interest; here the LED.

In the first image of the sequence, the focus point was moved just behind the LED and we see a similar image as when the focus point was placed between the matchstick and the LED. But now the rays have actually crisscrossed which is not observed here since the cone is symmetric. To demonstrate the crisscross nature, I placed an opaque object and covered the left half of the lens, which made the right semicircle of the circular projection of the cone, disappear! To come back to our proper cone I moved the focus point back to the matchstick and did the same experiment. Now covering the left portion of the lens masks the left semicircle of the LED! This means there no crisscross!

Computer Vision (24) and Optics

Even though light is traveling in 3D space, a sensor represents it on a 2D surface. Effectively what it captures is the state of light at a particular 2D plane, which is dependent on where the lens is focused. This is something that is unique; if you change the focus of your lens and the plane that you will be selecting to capture on your sensor will change automatically. Changing the plane means, selecting a plane at a different distance from the lens. This is why focus or accommodation is said to give the depth of the object when it is focused on to it.

If you closely observe the three sequence of pictures I had in my earlier post you will understand it easily. In the first image the focus point was at the match stick, and the LED was at a distance behind it. The light rays diverging from this source from the perspective of the aperture of the lens would be a 3D cone which will be truncated at the matchstick. This is what is giving you that circular patch. As I move the focus back, this circle gets smaller and the intensity increases. The light that is reflected and diverging from the matchstick is now captured at a different plane, which makes it blur. Finally, when the focus point is moved to the plane of the led, it is recovered completely, even though it was masked by the matchstick completely from the projection perspective of the camera. Due to further increase in the distance of the focus point, the matchstick becomes even more blur.

Computer Vision (23) and Optics

The best place to observe these things is in a mirror. You will be able to see any point around you at a specific place on the mirror by positioning yourself properly. This means that there are at least some rays from every point in space reaching the selected point on the mirror from where you are able to see that point in space.

I performed a series of experiments to understand focus and the behavior of light, which I will unravel here:

SECTION1: The green light source was placed at a certain distance from the match stick. Even though the match stick had completely blocked the 2D space or projection of the light source which was an led, it is completely recovered when the focus point is shifted from the match stick to the led.

From the perspective of our eye or the camera, the light source forms a 3D cone; the apex of which is at the source itself and the base at the lens or our eye. This is the reason you see a larger circle patch of green light when the match stick is focused, which is at a distance from the led. It is like truncating the 3D cone at a particular distance from its apex. Depending on at what distance from the apex you are truncating you will be getting circles of different diameters. Larger the diameter lesser will be the intensity of the light, because the energy has now spread out.

If you take the focus point to the surface of the lens, you will see that the diameter of the circle will be the same as the diameter of the aperture of the lens.

Computer Vision (22) and Optics

If I take a point source and place it in space it would emit light spherically in all directions around it. You will be able to see a point, only if the rays from that point reach your eyes. This means that you will be able to see a point source from any place around it. If u just had a sensor (retina) and not the lens in your eye, these rays that are diverging and almost everywhere in space would fall all over the retina to form an image which would be a uniform light patch in your brain. The same applies to non light sources as well. You will be able to see an object only if the object is reflecting light in the direction you are seeing. Again an object can reflect light in almost any direction around it. Without the lens, the reflected light from many points around you can fall at the same place on the retina as shown below.

The intensity and frequency of the reflected light from these various points can be different and hence get summed up at a point on the retina. This scenario can happen for every pixel on the sensor and hence the image that you will get will just be the summation of the intensities and frequencies of the rays coming out from various points around you. As a result of this you will always end up with a uniform patch of light on the sensor if you try to take an image without a lens.

If you didn’t have a lens in your eyes, you would only be able to know the amount of light present in the surrounding and not the objects present in front of you. The various objects wouldn’t be distinguishable at all.

To see a point as a point, we need to converge the rays that are diverging from it, to a point again. The lens does exactly this. Your brain sees various objects around it as they are because your eye lens converge the rays coming from it on the retina.