Cardinal Points and the Novel Imaging Properties of a Holographic System*

Reinhard W. Meier

doi:10.1364/JOSA.56.000219

Journal of the Optical Society of America
Vol. 56,
Issue 2,
pp. 219-223
(1966)
•https://doi.org/10.1364/JOSA.56.000219

Cardinal Points and the Novel Imaging Properties of a Holographic System

Reinhard W. Meier

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Reinhard W. Meier, "Cardinal Points and the Novel Imaging Properties of a Holographic System*," J. Opt. Soc. Am. 56, 219-223 (1966)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

The cardinal points (principal foci, principal planes, and nodal points) as well as the focal lengths of a holographic system are established by considering holographic imaging as a projective transformation between object and image space. Expressions for the coordinates of the cardinal points are given in terms of holographic variables, and they are compared with the corresponding expressions for a thin lens. The wavelength ratio between reconstructing and recording light in holography is found to correspond to the refractive index ratio between object and image space in conventional imaging, while the enlargement factor of the hologram has no analogue. The peculiar properties of the conjugate image, real or virtual, are discussed and related to the locations of the cardinal points for the conjugate imaging system.

Full Article | PDF Article

More Like This

Optical Properties of Holographic Images

Reinhaed W. Meier
J. Opt. Soc. Am. 57(7) 895-900 (1967)

Image Luminance and Ray Tracing in Holography

Carl W. Helstrom
J. Opt. Soc. Am. 56(4) 433-441 (1966)

Longitudinal Image Formation*

B. Roy Frieden
J. Opt. Soc. Am. 56(11) 1495-1501 (1966)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (6)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (18)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

	True image	Conjugate image
a₀	0	0
b₀	0	0
c₀	m²z_r − μz_c	m²z_r + μz_c
d₀	μz_cz_r	−μz_cz_r

a₁	μmz_cz_r	−μmz_cz_r
b₁	0	0
c₁	m²x_cz_r − μmx_rz_c	m²x_cz_r + μmx_rz_c
d₁	0	0

a₂	0	0
b₂	μmz_cz_r	−μmz_cz_r
c₂	m²y_cz_r − μmy_rz_c	m²y_cz_r + μmy_rz_c
d₂	0	0

a₃	0	0
b₃	0	0
c₃	m²z_cz_r	m²z_cz_r
d₃	0	0

	Object space	Image space
Thin lens	$\frac{- μ r_{1} r_{2}}{(\frac{n_{2} - n_{1}}{n_{2}}) r_{1} - (\frac{n_{0} - n_{1}}{n_{0}}) μ r_{2}}$	$\frac{r_{1} r_{2}}{(\frac{n_{2} - n_{1}}{n_{2}}) r_{1} - (\frac{n_{0} - n_{1}}{n_{0}}) μ r_{2}}$

True image	$\frac{- μ z_{r} z_{c}}{m^{2} z_{r} - μ z_{c}}$	$\frac{m^{2} z_{r} z_{c}}{m^{2} z_{r} - μ z_{c}}$

Conjugate image	$\frac{- μ z_{r} z_{c}}{m^{2} z_{r} + μ z_{c}}$	$\frac{m^{2} z_{r} z_{c}}{m^{2} z_{r} + μ z_{c}}$

	Object space	Image space
True image	$\frac{m x_{c} z_{r} - μ x_{r} z_{c}}{m^{2} z_{r} - μ z_{c}}$	$\frac{m^{2} x_{c} z_{r} - μ m x_{r} z_{c}}{m^{2} z_{r} - μ z_{c}}$

Conjugate image	$\frac{m x_{c} z_{r} + μ x_{r} z_{c}}{m^{2} z_{r} + μ z_{c}}$	$\frac{m^{2} x_{c} z_{r} + μ m x_{r} z_{c}}{m^{2} z_{r} + μ z_{c}}$

	Object space	Image space
Thin lens	0	0

True image	$\frac{μ z_{r} z_{c} (m - 1)}{m^{2} z_{r} - μ z_{c}}$	$\frac{m z_{r} z_{c} (m - 1)}{m^{2} z_{r} - μ z_{c}}$

Conjugate image	$- \frac{μ z_{r} z_{c} (m - 1)}{m^{2} z_{r} + μ z_{c}}$	$\frac{m z_{r} z_{c} (m - 1)}{m^{2} z_{r} + μ z_{c}}$

	Object space	Image space
Thin lens	$\frac{r_{1} r_{2} (1 - μ)}{(\frac{n_{2} - n_{1}}{n_{2}}) r_{1} - (\frac{n_{0} - n_{1}}{n_{0}}) μ r_{2}}$	$\frac{r_{1} r_{2} (1 - μ)}{(\frac{n_{2} - n_{1}}{n_{2}}) r_{1} - (\frac{n_{0} - n_{1}}{n_{0}}) μ r_{2}}$

True image	$\frac{z_{r} z_{c} (m - μ)}{m^{2} z_{r} - μ z_{c}}$	$\frac{m z_{r} z_{c} (m - μ)}{m^{2} z_{r} - μ z_{c}}$

Conjugate image	$\frac{z_{r} z_{c} (m + μ)}{m^{2} z_{r} + μ z_{c}}$	$\frac{m z_{r} z_{c} (m + μ)}{m^{2} z_{r} + μ z_{c}}$

	Object space	Image space
Thin lens	$(\frac{n_{2} - n_{1}}{n_{2}}) \frac{1}{μ r_{2}} - (\frac{n_{0} - n_{1}}{n_{0}}) \frac{1}{r_{1}}$	$- (\frac{n^{2} - n_{1}}{n_{2}}) \frac{1}{r_{2}} + (\frac{n_{0} - n_{1}}{n_{0}}) \frac{μ}{r_{1}}$

True image	$\frac{m}{μ z_{c}} - \frac{1}{m z_{r}}$	$- \frac{m}{z_{c}} + \frac{μ}{m z_{r}}$

Conjugate image	$- \frac{m}{μ z_{c}} - \frac{1}{m z_{r}}$	$- \frac{m}{z_{c}} - \frac{μ}{m z_{r}}$

Abstract

Cited By

Tables (6)

Equations (18)

Journal of the Optical Society of America