Talk:Ray transfer matrix analysis

message: There appears to be a contradiction in this page.
1) From a thermodynamic consideration, AD-BC=1
2) The ray transfer matrix for a beam going from refractive index n1 to n2 is given by:
A=1, B=0, C=0 and D=n1/n2
This gives  AD-BC=n1/n2
which is not equal to 1 in most cases.
I have been looking into this a bit, but still have no idea what the answer is.
: So after reading Siegman's Lasers (Ch. 15) I learnt that in general AD-BC = n1/n2, which explains everything.  I revised the article.  Good catch.  -- Pgabolde 15:59, 17 February 2006 (UTC)

message: Among those that work with optics and especially systems of the aforementioned, these equations are used daily. Yet, they are rarely incoporated into grade/high school academics. Because this is used on a daily basis in the optics field but rarely taught in schools I believe it should recieve a "mid" ranking. --Frozenport (talk) 01:12, 26 June 2008 (UTC)
thread_title:  Importance 

message: I suggest renaming this article "Matrix formalism (optics)". I believe this is simpler, and perhaps more common name than "Ray transfer matrix analysis".
Ahmes 10:31, 20 May 2006 (UTC)
thread_title:  Renaming the article 

message: In the table it says: "In Propagation in free space or in a medium of constant refractive index" and the matrix: (1 d)(0 1)
But in a dielectric I think it is (1 d/n)(0 1) where n is the refractive index. So is it right to write "or in a medium of constant refractive index"?
* The propagation in free space is the same as the propagation in a medium with a constant refractive index. i edited the remark for the translation matrix in the table of the ray transfer matrizes. See here. Here is an example of the method: http://www.ee.byu.edu/cleanroom/ABCD_Matrix_tut.phtml --141.35.186.111 19:46, 8 August 2007 (UTC)
thread_title:  Error in table? 

message: This appears to be either incorrect or poorly defined. This identity matrix {{1,0},{0,1}} indeed describes reflection from a flat mirror, but only a flat mirror with a face parallel to the z plane (where the ABCD matrices are normally defined in a cartesian plane with z representing the horizontal direction, r representing the vertical direction, and theta being defined as delta r/delta z). If the mirror face is parallel to the r plane (the more common occurrence) the matrix would be {{1,0},{0,-1}}. None of this accounts for a mirror of arbitrary angle.
--71.178.207.74 (talk) 00:37, 20 January 2009 (UTC)
thread_title:  reflection from flat mirror 

message: The articles includes two examples of Gaussian Beam propagation, through free space and a thin lens.  Both have a statement afterward regarding the radius, but the statements are incorrect in the general case, and for any condition of which the statements are reasonable, there is no additional context provided so that the intended meaning is rather useless and/or misleading.  Because an in-depth explanation is probably not appropriate for the article, I plan on removing the statements altogether unless someone shares a good explanation.  My own arguments follow:
===== Free space: =====
The free-space example concludes with q_2 = q_1+d and then says "traveling through free space increases the radius by d".  But the wave-front radius is only related to the real part of the reciprocal of the q parameter, not the real part of the q parameter itself.  Although the q parameter can be defined like in the article as its reciprocal, the q parameter can also be defined like q = \delta z + i\ z_R, where z_R is the Raleigh length and \delta z represents a displacement from the beam waist.  In this view, we have that \delta z_2 = \delta z_1 + d.  Regarding the wave-front radius, some complex algebra tells us that \frac{1}{R_1} = \frac{\delta z}{{\delta z}^2 + z_R^2} and \frac{1}{R_2} = \frac{\delta z + d}{{(\delta z + d)}^2 + z_R^2}.  Only when d \gg z_R and \delta z_1 \neq 0 is the statement in question applicable, but when working with collimated beams (or nearly so), the Rayleigh length z_R is not small especially compared to free-space propagation distances.  That statement is also meaningless when starting the beam propagation from the waist where \delta z_1 = 0 and the radius is infinite (i.e. a wave front is a planar surface).
===== Thin lens: =====
The comment for this examples says "Again, only the real part of q is affected: the radius of curvature is reduced by 1/f."  But this time, rather than the real part of q itself, it is the real part of the reciprocal that changes.  They are not the same thing and its incorrect to just casually refer to them as the same thing.  The real and imaginary parts of the q parameter and separately its reciprocal have different interpretations.  Likewise, the reciprocal of the radius is reduced by 1/f, not the radius.  Re[\frac{1}{q_2}] = Re[\frac{1}{q_1}] - \frac{1}{f} = \frac{1}{R_1} - \frac{1}{f} .  (A little algebra shows that the radius is really "reduced" by \frac{R_1^2}{f - R_1}.)
cperk (talk) 14:08, 16 July 2015 (UTC)
thread_title:  Comments for Examples in Gaussian Beam section 

message: The comment for this examples says "Again, only the real part of q is affected: the radius of curvature is reduced by 1/f."  But this time, rather than the real part of q itself, it is the real part of the reciprocal that changes.  They are not the same thing and its incorrect to just casually refer to them as the same thing.  The real and imaginary parts of the q parameter and separately its reciprocal have different interpretations.  Likewise, the reciprocal of the radius is reduced by 1/f, not the radius.  Re[\frac{1}{q_2}] = Re[\frac{1}{q_1}] - \frac{1}{f} = \frac{1}{R_1} - \frac{1}{f} .  (A little algebra shows that the radius is really "reduced" by \frac{R_1^2}{f - R_1}.)
cperk (talk) 14:08, 16 July 2015 (UTC)
thread_title:  Thin lens: 

message: The angles are measured as slopes, which is mentioned nowhere and not obvious at all. Sure, everyone will figure out its measured neither in degrees nor rad. But that the slope belongs there is not clear from the drawings.
The german article luckily explicitly mentions that. I've never seen a slope being indicated in a drawing like an angle. That's horribly confusing.  — Preceding unsigned comment added by 129.69.48.35 (talk) 15:50, 19 November 2019 (UTC)
thread_title:  Angles Theta 

message: As we all know, there are various systems for laying out the matrices: 
e.g. Meyer-Arendt, Hecht, Gerrard/Busch.  They differ in sign conventions
but also in order of the elements A, B, C, D.  The choice is a matter
of personal preference.  The article should say which system it is using,
and note that there are other systems.  Don't leave the reader wondering
why it doesn't match the textbook he happens to be using, or poking around
in the citations for clues.  (If there is now some optical industry standard 
governing this, I guess I haven't heard about it.) Mgryan (talk) 21:40, 15 March 2024 (UTC)
thread_title:  Which matrix format?