1. Image formation

2. Camera: optical system
da=a -a 2 1
curvature radius r r Z 1 2
thin lens
small angles:

3. Y
incident light beam
lens refraction index: n
deviated beam Z
deviation angle ? Dq = q’’-q

4. Thin lens rules a) Y=0  Dq = 0 f Dq
beams through lens center: undeviated
b) f Dq = Y 
independent of y
parallel rays converge onto a focal plane Y f Dq

5. f r Where do all rays starting from a scene point P converge ? P Y O Z
Fresnel law
Obs. For Z  ∞, r  f

6. f d if d ≠ r … image of a point = blurring circle image plane Z P O a
F(blurring circle)=a (d-r)/r r
focussed image:
F(blurring circle) <image resolution d
depth of field: range [Z1, Z2] where image is focussed

7. Hp: Z >> a
r  f
the image of a point P belongs to the line (P,O) P
image plane O p
p = image of P = image plane ∩ line(O,P)
interpretation line of p: line(O,p) =
locus of the scene points projecting onto image point p

8. Until here:
where goes light ?
But:
how much light does reach an image point?

9. Image Formation: Reflectance Map
Simplified model:
light originates at a source
light is reflected by an object
light collected by camera lens and focused to image
[adapted from Hemant D. Tagare]

10. Reflectance Map dA at P receives flux of d watt: Irradiance at P:
(watt/meter2,
spatial density of flux at P)

11. reflectance map ctd.
d infinitesimal solid angle, centered along incident direction
infinitesimal flux d2 passes through it, incident on dA
,: zenith,azimuth
dA cos : fore-shortened area dAf
Radiance of incident flux:
Units: watt per m2 per steradian

12. reflectance map ctd.
Radiant intensity of flux:
Object is a point (no area)
flux d incident on it from solid angle d
units: watt per steradian

13. Solid Angle Solid angle d: solid angle centered around direction ,
spherical geometry: dA = r2 sin dd

14. Computation of flux Flux :
irradiance E and radiance L are derivatives of flux  flux comp. as integral
L(P,,): radiance along , at any point P of surface
E(P): irradiance at P
: net flux received by object
and,

15. Generalization: Reflected Light
so far: radiance and radiant intensity defined in terms of incident light
definitions also apply to reflected / emitted light  flux d is assumed to have reverse direction (leaves surface)
radiance of reflected light (dA through d) :

16. a f Z
image intensity: proportional to irradiance E
where
is the radiance reflected towards the lens