70
2 Holographic Microscopy of Phase and Diffuse Objects …
as well as diffusely scattering surfaces concerning deformations analysis was developed in the works [56, 57, 65, 158, 159]. Unlike other schemes of holographic
interferometry, the presence of the microobjective is necessary here. The influence
of the objective on interference pattern forming was studied by a number of authors
[160, 161]. So, it becomes interesting to study the influence of defocusing on field
amplitude correlations on which the form of holographic interferograms depends.
The objective can differently influence interference pattern formation. Some
authors [133, 134, 162–164] paid their attention to the dependence of interferograms contrast on optical system aperture. In single works [165], phase difference
between interfering waves is considered as an aperture function. Though in many
cases, this change is small (about λ/4), with the appearance of the possibility for
high-accuracy measurements, the necessity appears to take into account the sources
of even small mistakes. Moreover, the image phase depends on the used microscopic
objective, especially when the sizes of the objects are close to the resolution limit
as is shown in [166]. Phase distribution in small phase asperity image is calculated
there.
In the work [167], the dependence of interference pattern contrast on the magnification is being discussed, and in the work [168], the attempt of considerable increase
in the sensitivity by using optical system longitudinal magnification is grounded.
The defocusing problem, connected with the use of the objective is the following. If
the object is shifted along the optical axis as the result of deformation, then it transcends the focusing plane. Three-dimensional shift vector
d describing deformation
is usually taken into account only in the expression for the reflecting wave phase, and
the change of pulse response for the analysis simplification is neglected even in such
generalized studies as [162]. And with it, in the works [169–171], it is clearly shown
that during defocusing the image itself considerably changes, and as a result, the
interference pattern where there is a defocused image for transparency, phase and
diffusive objects—should be also changed. In native and foreign literatures, there
is almost no quantitative analysis of such studies. At the best, it is noticed that in
the result of deformation, the object should not transcend objective contrast. It is
quite obvious that during one and the same shift, defocusing will be different for
different objectives, in particular, for microobjectives with small focusing distance,
because even small shift leads to considerable defocusing. In such conditions, it is
quite problematic to study strongly defocused or excited structures, for example,
muscle fibers.
Let us consider the scheme of holographic interference microscope shown in
Fig. 2.5a in detail. In its initial state, the object is in the plane x 0 0y 0 described by
two-dimensional vector
x 0 = (x 0 , y 0 ) at a distance d 0 from the objective entrance
pupil O b , which forms the image in the plane x i 0y i ,
x i = (x i , y i ).
If U 1 ( x o ) is the field distribution behind the object O, and h( x i − M
x 0 , d z ) is the
pulse response of isoplanatic objective depending in general on the defocusing value
d z , then in the image plane, the field distribution will be defined by (2.1)
2 Holographic Microscopy of Phase and Diffuse Objects …
as well as diffusely scattering surfaces concerning deformations analysis was developed in the works [56, 57, 65, 158, 159]. Unlike other schemes of holographic
interferometry, the presence of the microobjective is necessary here. The influence
of the objective on interference pattern forming was studied by a number of authors
[160, 161]. So, it becomes interesting to study the influence of defocusing on field
amplitude correlations on which the form of holographic interferograms depends.
The objective can differently influence interference pattern formation. Some
authors [133, 134, 162–164] paid their attention to the dependence of interferograms contrast on optical system aperture. In single works [165], phase difference
between interfering waves is considered as an aperture function. Though in many
cases, this change is small (about λ/4), with the appearance of the possibility for
high-accuracy measurements, the necessity appears to take into account the sources
of even small mistakes. Moreover, the image phase depends on the used microscopic
objective, especially when the sizes of the objects are close to the resolution limit
as is shown in [166]. Phase distribution in small phase asperity image is calculated
there.
In the work [167], the dependence of interference pattern contrast on the magnification is being discussed, and in the work [168], the attempt of considerable increase
in the sensitivity by using optical system longitudinal magnification is grounded.
The defocusing problem, connected with the use of the objective is the following. If
the object is shifted along the optical axis as the result of deformation, then it transcends the focusing plane. Three-dimensional shift vector
d describing deformation
is usually taken into account only in the expression for the reflecting wave phase, and
the change of pulse response for the analysis simplification is neglected even in such
generalized studies as [162]. And with it, in the works [169–171], it is clearly shown
that during defocusing the image itself considerably changes, and as a result, the
interference pattern where there is a defocused image for transparency, phase and
diffusive objects—should be also changed. In native and foreign literatures, there
is almost no quantitative analysis of such studies. At the best, it is noticed that in
the result of deformation, the object should not transcend objective contrast. It is
quite obvious that during one and the same shift, defocusing will be different for
different objectives, in particular, for microobjectives with small focusing distance,
because even small shift leads to considerable defocusing. In such conditions, it is
quite problematic to study strongly defocused or excited structures, for example,
muscle fibers.
Let us consider the scheme of holographic interference microscope shown in
Fig. 2.5a in detail. In its initial state, the object is in the plane x 0 0y 0 described by
two-dimensional vector
x 0 = (x 0 , y 0 ) at a distance d 0 from the objective entrance
pupil O b , which forms the image in the plane x i 0y i ,
x i = (x i , y i ).
If U 1 ( x o ) is the field distribution behind the object O, and h( x i − M
x 0 , d z ) is the
pulse response of isoplanatic objective depending in general on the defocusing value
d z , then in the image plane, the field distribution will be defined by (2.1)