Radius v/s Clear Semi-Diameter in Zemax OpticStudio

- In Zemax, Radius defines how curved is the lens surface. This value is 'infinity' for a flat surface.

- Whereas the Clear Semi-Diameter defines how big is the optic/lens. Its is the vertical distance from the optic axis to the periphery. Because for radius values very large, we cannot have a camera infinitely tall!

Snell's Law and Fermat's Principle

Snell's Law:

n1 * sin(theta_1) = n2 * sin(theta_2)

Fermat's Principle:

Light rays take the path that requires the least travel time.

Fraser's Spiral

 

(Image Source: Wikipedia)

It turns out that there is actually no spiral in the above image. The above image only has concentric circles. The spiral is just an incorrect human perception. This is called the Fraser's Spiral!

"While there is no computer vision system that is as versatile as the human vision system as of today; there are many computer vision systems that are more precise and reliable than the human vision system. In short, for many tasks that require vision the human vision system might be the wrong system to emulate. Furthermore, human visual system is more fallible than we would like to believe." - Dr. Shree K. Nayar

Importance of Luminance and Chrominance in Image Processing

    The human eye is more sensitive to the luminance(brightness) in an image as compared to the chrominance(color) information in an image. Thus, image recovery algorithms define a cost function in such a way that the regularization term applied to luminance component tries to preserve edges(high frequency information), while the regularization term applied to the chrominance component tries to ensure smoothness. The chrominance regularization thus removes color artifacts which are more sensitive and objectionable to the human eye.

(Source: S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” International Journal of Imaging Systems and Technology 14, 47–57 (2004).)

Field Number of a Microscope

    For typical objective lenses in a microscope, the magnification range is from 10X to 100X. These objectives form an intermediate image which is a circle, typically 50-60mm in diameter. Out of this circular image, only 19-23mm from the center is well corrected for aberrations. The ocular/eyepiece clips the image to this inner diameter which is called as the Field Number of a Microscope.

(Source: M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings of ACM SIGGRAPH. (2006) 924–934.)

Mean and Expected Value

The mean and expected values are closely related but there is a difference.

For example, we have 5 coins with 2 coins of five cents and 3 coins of 10 cents respectively. In this case, we calculate the mean by averaging the coin's values as Cmean = (1/5)*(5+5+10+10+10) = 8. Here, 8 is the Mean and not the expected value as the system state (coin's value) is not hidden.

Now, we have five different weight measures of the same person as: 79.8kg, 80kg, 80.1kg, 79.8kg, and 80.2kg. Here, the person is a system and the person's weight is the system's state. The measurements are different due to random errors in the weight scales and therefore the persons weight is a hidden state. We do not know the exact value of the person's weight but can make an estimate by averaging the scale's measurements as Wavg = (1/5)*(79.8 + 80 + 80.1 + 79.8 + 80.2) = 79.98kg. The outcome of this estimate is called the Expected Value.

(Source: https://www.kalmanfilter.net/background.html)

Human Eye has a Blind Spot

    The human eye has a blind spot on the retina, meaning there are no image sensors(rods and/or cones) in this region. This is the place where image gets transferred to the brain using optic nerves. To realize this blind spot, draw a cross and a circle at two distinct ends on a piece of paper respectively. Now, close your one eye and move back and forth while continuously focusing on the cross. At a certain point, the circle disappears from your vision and this is because the circle’s image was formed at the location of your blind spot. If you further continue moving in the direction you were already moving, the circle appears again.