imaging + signalling

Question 1

number of alternatives for a b number of bits?

Answer 1

N = 2^b

where:
• N = number of alternatives
• b = number of bits

Question 2

number of bits needed for N number of alternatives?

Answer 2

b = log{2}(N)

where:
• b = number of bits
• N = number of alternatives [aka alternative quantisation levels]

Question 3

how to figure out the number of useful levels?

Answer 3

number of useful levels = V total/V noise

where:
• V total = total voltage range used by signal (INCLUDING NOISE) (max + min of y-axis)
• V noise = range of voltage on signal used by noise (max + min on y-axis for noise)

Question 4

how to calculate out [max] number of bits you should use to sample signal?

Answer 4

b max = log{2}(V total max/V noise max)

where:
• b max = max number of bits you can use to sample signal
• V total max = max range of voltage used by signal
• V noise max = max range of voltage used by noise

Question 5

what is the equation for the refractive index (n) for light travelling from a vacuum into a medium? (v,c)

Answer 5

refractive index = speed of light in vacuum/speed of light in medium

n = c/v

Question 6

equation for refractive index (n) for light travelling from a vacuum into a medium? (c, v, θi and θr)

Answer 6

n = speed of light in vacuum/wavelength of light in medium = sinθi/sinθr

Question 7

what is snell’s law? (n1, n2, sinθi, sinθr)

Answer 7

n1sinθi = n2sinθr

Question 8

equation for curvature? (using r)

Answer 8

curvature = 1/r

where radius (r) of curvature is focal length (f) of lens (for plane wavefronts entering convex lens)

Question 9

equation for lens power? (using f)

Answer 9

lens power = 1/f

where f = focal length

Question 10

lens equation? (v, u, f)

Answer 10

1/v = 1/u + 1/f

(u is ALWAYS negative)

Question 11

equation for magnification (m)? (v, u)

Answer 11

m = v/u

where v = image distance and u = object distance

Question 12

equation for magnification (m)? (object height, image height)

Answer 12

m = image height/object height

Question 13

equation for resolution? (length of object, no. pixels across object)

Answer 13

resolution = true length of object/no. of pixels across object

Question 14

equation for amount of information[/data] in image?

Answer 14

amount of information in image = number of pixels x bits per pixel

Question 15

wave equation? (v, f, λ)

Answer 15

wave speed = frequency x wavelength

v = fλ

Question 16

nyquist’s theorem?

Answer 16

sampling f > 2 x f of smallest important change
OR
sampling f > 2 x highest f

Question 17

equation to work out number of quantisation levels needed per sample?

Answer 17

no. of quantisation levels needed per sample = Vtotal/Vnoise

Question 18

equation to work out number of bits (b) needed to sample signal?

Answer 18

b = log(2)[Vtotal/Vnoise]

^also known as shannon’s criteria

Question 19

equation for resolution of sampled signal?

Answer 19

resolution = range of variation of signal/number of quantisation levels

remember no. of quantisation levels = 2^b

Question 20

equation for transmission rate?

Answer 20

transmission rate of info = f of sample x bits or bytes per sample
OR
transmission rate of info = total info sent [in bits, bytes, etc]/time taken

Question 21

rule for θi and θr?

Answer 21

when light moving from less optically dense material to more optically dense material:

θi > θr