You see, you have to be an expert on the Sagnac effect in order to understand all of the subtleties, to have access to references which will explain all of your questions.
G. Malykin's treatise has over 300 references, and yet, it missed one of the most important ones, a paper published by Dr. Silberstein in 1922.
In 1922, Dr. Silberstein published a second paper on the subject, where he generalizes the nature of the rays arriving from the collimator:
http://gsjournal.net/Science-Journals/Historical%20Papers-Mechanics%20/%20Electrodynamics/Download/2645This paper explains the issue raised by Malykin, but evidently missed by him.
Moreover, it is Malykin who makes a tremendous error in comparing the Sagnac effect with the effect predicted by special relativity.
The Sagnac effect is far larger than the effect forecast by relativity theory.
STR has no possible function in explaining the Sagnac effect.
The Sagnac effect is a non-relativistic effect.
COMPARISON OF THE SAGNAC EFFECT WITH SPECIAL RELATIVITY, starts on page 7, calculations/formulas on page 8
http://www.naturalphilosophy.org/pdf/ebooks/Kelly-TimeandtheSpeedofLight.pdfpage 8
Because many investigators claim that the
Sagnac effect is made explicable by using the
Theory of Special Relativity, a comparison of
that theory with the actual test results is given
below. It will be shown that the effects
calculated under these two theories are of very
different orders of magnitude, and that
therefore the Special Theory is of no value in
trying to explain the effect.
COMPARISON OF THE SAGNAC EFFECT WITH STR
STR stipulates that the time t' recorded by an observer moving at velocity v is slower than the time t
o recorded by a stationary observer, according to:
t
o = t'γ
where γ = (1 - v
2/c
2)
-1/2 = 1 + v
2/2c
2 + O(v/c)
4...
t
o = t'(1 + v
2/2c
2)
dt
R = (t
o - t')/t
o = v
2/(v
2 + 2c
2)
dt
R = relativity time ratio
Now, t
o - t' = 2πr/c - 2πr/(c + v) = 2πrv/(c + v)c
dt' = t
o - t' = t
ov/(c + v)
dt
S = (t
o - t')/t
o = v/(v + c)
dt
S = Sagnac ratio
dt
S/dt
R = (2c
2 + v
2)/v(v + c)
When v is small as compared to c, as is the case in all practical experiments, this ratio
reduces to 2c/v.
Thus the Sagnac effect is far larger than any
purely Relativistic effect. For example,
considering the data in the Pogany test (8 ),
where the rim of the disc was moving with a
velocity of 25 m/s, the ratio dtS/dtR is about
1.5 x 10^7. Any attempt to explain the Sagnac
as a Relativistic effect is thus useless, as it is
smaller by a factor of 10^7.
Referring back to equation (I), consider a disc
of radius one kilometre. In this case a fringe
shift of one fringe is achieved with a velocity
at the perimeter of the disc of 0.013m/s. This
is an extremely low velocity, being less than
lm per minute. In this case the Sagnac effect
would be 50 billion times larger than the
calculated effect under the Relativity Theory.
Post (1967) shows that the two (Sagnac and STR) are of very different orders of magnitude. He says that the dilation factor to be applied under SR is “indistinguishable with presently available equipment” and “is still one order smaller than the Doppler correction, which occurs when observing fringe shifts” in the Sagnac tests. He also points out that the Doppler effect “is v/c times smaller than the effect one wants to observe." Here Post states that the effect forecast by SR, for the time dilation aboard a moving object, is far smaller than the effect to be observed in a Sagnac test.