【Engineering Optics】Beam Confinement of Optical Systems

ref "Engineering Optics" fifth edition Yu Daoyin

1. Aperture

Aperture diaphragm

• A diaphragm that limits the imaging beam width of the on-axis object point, and has the function of selecting the position of the imaging beam of the off-axis object point
• Entrance pupil : Aperture diaphragm is imaged in object space through the front light group
  • The hole ~ at the front of the system itself is the entrance pupil
  • and the aperture stop conjugate with respect to the preceding light group
• Exit pupil : Aperture diaphragm is imaged in image space through the rear light group
  • The hole at the rear of the system is itself the exit pupil
  • and the aperture stop conjugate with respect to the light group behind
  • The exit pupil and the entrance pupil are conjugate with respect to the entire optical system
• Object Aperture Angle : On-axis Object Point – Entrance Pupil Edge $\angle Optical$ axis
• Image square aperture angle : on-axis image point – exit pupil edge $\angle Optical$ axis

Field diaphragm

• Aperture that limits the imaging range of object plane/object space
• Entrance window : The field diaphragm is imaged in object space by the light group in front
  • View ~ in the front of the system itself as a window
  • Conjugate with the field diaphragm with respect to the front light group
• Out the window : The field diaphragm is imaged in the image space by the light group behind
  • Depending on the ~ at the back of the system itself as a window
  • Conjugate with the field diaphragm with respect to the light group behind
  • The exit window and the entrance window are conjugated with respect to the entire optical system
• Object field angle : center of entrance pupil – edge of entrance window $\angle Optical$ axis
• Image field angle : center of exit pupil – edge of exit window $\angle Optical$ axis

Vignetting

• The beam filling the entrance pupil is blocked, the actual imaging beam width at the off-axis point < the on-axis point, the edge of the image surface is darker than the center
• Vignetting Stop: A stop that acts as vignetting
• Vignetting factor
  • $$K_{}=\frac{D_{}}{D}$$

Judgment diaphragm

Optical system

camera system

• Composition: photographic objective, iris diaphragm, photosensitive film
• Camera: Aperture ↓, Depth of Field ↑; Aperture ↑, Depth of Field ↓

Telescope system

Kepler telescope

• Positive lens + positive lens = afocal system
• Objects at infinity are inverted

Galileo telescope

• Positive Lens + Negative Lens = Afocal System
• no real image surface
• Infinity objects are erected

Microsystem

• Features
  • Positive lens + positive lens
  • Objective and eyepiece focal length
  • Optical separation $\Delta$ large

Beam Confinement in Biological Microscopy

Measuring the beam limitation of microscopes

• The aperture diaphragm is in the image-side focal plane, forming an object-side telecentric optical path
  • Avoid measurement errors caused by inaccurate focusing

object-side telecentric light path

pupil connection

The exit pupil/window of the front light group <-> the entrance pupil/entry window of the rear light group to avoid pupil cutting

field lens

• Lenses placed near the real/real image plane in an optical system
• Connect the pupils of the front and rear systems to reduce the aperture of the optical components
• Variety
  • Exit pupil size does not change
  • exit pupil distance
  • visual magnification
  • Vignetting factor $\uparrow$

depth of field

• Vision
  • $$D_{}=p_{}-p=\frac{p^2}{2a-p\epsilon }$$
• close-up
  • $$D_{}=p-p_{}=\frac{p^2}{2a+p\epsilon }$$
• $D=D_{}+D_{}$