Optical: systems and elements – Diffraction – From grating
Reexamination Certificate
1998-12-23
2001-05-29
Henry, Jon (Department: 2872)
Optical: systems and elements
Diffraction
From grating
C359S566000, C359S558000, C359S577000
Reexamination Certificate
active
06239909
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an image-forming method and an image-forming apparatus. More particularly, the present invention relates to an image-forming method that uses a microscope. The present invention also relates to an image-forming apparatus using a microscope.
2. Description of Related Art
In image formation by an image-forming optical system, e.g. an optical microscope, a transfer function unique to each particular image-forming optical system exists as detailed in J. W. Goodman, “Introduction to Fourier Optics”, McGraw-Hill (1968) by way of example. The characteristics of an object image formed by an image-forming optical system is limited by the transfer function. More specifically, among Fourier components (spatial frequency components) of an optical image to be transferred by an image-forming optical system, only those in a specific spatial frequency region determined by the transfer function of the image-forming optical system are transferred, and the remaining spatial frequency components are cut off.
For example, in an ordinary optical microscope, a spatial frequency f
cutoff
exists, which is determined by the numerical aperture (NA) of the objective and known as “cutoff frequency”:
f
cutoff
=2NA/&lgr; (1)
(where &lgr; is the wavelength of light)
Among the Fourier components of an input optical image, spatial frequency components higher than the cutoff frequency are cut off and hence cannot be reflected in image formation.
As shown in
FIG. 12
in the accompanying drawings, the numerical aperture of an objective
1
is determined by multiplying together the sine function of ½ of the apex angle of the cone of light
2
that the objective
1
can take in from an observation object O and the refractive index of the medium between the observation object O and the front surface of the objective
1
. For an object in the air, for example, the numerical aperture does not become more than 1. Therefore, the cutoff frequency does not become more than 2/&lgr;. Accordingly, ordinary optical microscopes cannot resolve a fine structure with a period smaller than ½ of the wavelength of light that is placed in the air.
However, spatial frequency components of an observation image in a spatial frequency region that cannot be transferred by an image-forming optical system can be reflected in image formation by inserting a spatial frequency-modulating device between the observation object and the image-forming optical system. In this case, however, the observation object image formed by the image-forming optical system has been modulated. Therefore, a correct observation object image is formed by jointly using a device for restoring the modulated image (i.e. a demodulating device). Application of this technique to an optical microscope makes it possible to resolve a fine structure of an observation object having a spatial frequency higher than the conventional cutoff frequency. This is referred to as “superresolution”.
W. Lukosz, “Optical systems with resolving powers exceeding the classical limit. II”, Journal of the Optical Society of America, Vol. 57, No. 7 (1967), pp. 932-941, discloses a method of obtaining superresolution by using a system arranged as shown in FIG.
19
. That is, diffraction gratings
5
and
6
having conjugate grating constants are placed at respective positions conjugate to each other. More specifically, the diffraction grating
5
is placed at a position between an observation object O and an image-forming optical system
3
and near the observation object O. The diffraction grating
6
is placed behind a position where an image of the observation object O is formed by the image-forming optical system
3
. With this arrangement, the diffraction gratings
5
and
6
are moved conjugably to thereby obtain superresolution. The diffraction grating
5
, which is placed near the observation object O, diffracts and thus modulates light emanating from the observation object O. The light emanating from the observation object O includes spatial frequency components having angles at which they cannot enter the image-forming optical system
3
. A part of such spatial frequency components are allowed to enter the image-forming optical system
3
by the modulation effected by the diffraction grating
5
. That is, the propagation angle of a part of the spatial frequency components is changed by the diffraction, and the modulated components enter the image-forming optical system
3
. The diffraction grating
5
produces a plurality of diffracted light beams. Therefore, an input image having a plurality of modulation components is transferred by the image-forming optical system
3
, and a modulated image
4
is formed at the image-formation position of the image-forming optical system
3
. The diffraction grating
6
, which is placed behind the image-formation position demodulates the modulated image
4
. More specifically, each modulation component having a propagation angle changed by the diffraction grating
5
near the observation object O is transferred by the image-forming optical system
3
and then passed through the diffraction grating
6
, thereby restoring the changed propagation angle to the original state to form a restored image. Thus, spatial frequency components that cannot be transferred by only the image-forming optical system
3
can also be reflected in image formation by combining the image-forming optical system
3
with the diffraction gratings
5
and
6
, and superresolution can be attained. However, W. Lukosz admits in the paper that it is not easy to realize such an arrangement and drive of diffraction gratings.
On the other hand, D. Mendlovic et. al., “One-dimensional superresolution optical system for temporally restricted objects”, Applied Optics, Vol. 36, No. 11 (1997), pp. 2353-2359, discloses that they were successful in an experiment designed to obtain superresolution with a single rotary diffraction grating
7
, as shown in
FIG. 20
, by using an arrangement in which an observation object O and a modulated image
4
of the observation object O, which is formed by an image-forming optical system
3
, are placed in approximately the same plane. However, in such an arrangement, the magnification of the image of the observation object O formed by the image-forming optical system
3
is substantially limited to −1.
FIG. 21
shows the arrangement of a novel optical system presented by Dr. Tony Wilson (University of Oxford, Oxford, UK) at the 20th Lecture Meeting of the Society for the Research of Laser Microscopes held on Nov. 7, 1997. The optical system includes a movable diffraction grating
8
, an illuminating optical system
9
that projects an image of the diffraction grating
8
on the focal position of an objective
1
, an image-forming optical system
3
that forms an enlarged image of an observation object O, a CCD
10
that detects the image of the observation object O formed by the image-forming optical system
3
, an image storage unit
11
that stores the image detected by the CCD
10
, an arithmetic unit
12
that performs an arithmetic operation using the image stored in the image storage unit
11
, and an image display unit
13
that displays the result of the arithmetic operation performed by the arithmetic unit
12
. A combination of the diffraction grating
8
and the illuminating optical system
9
illuminates the observation object O with illuminating light having a sinusoidal intensity distribution. Three images of the observation object O are detected by the CCD
10
in respective states where the spatial phases of the sine wave of the illuminating light on the observation object O are different from each other by 120 degrees. From the intensity distributions I
1
, I
2
and I
3
of the three images detected by the CCD
10
, a light-cut image I
c
is obtained by calculating the following equation:
I
c
={square root over ( )}{(
I
2
−I
1
)
2
+(
I
3
−I
2
)
2
+(
I
1
−I
3
)
2
}
Hayashi Shin'ichi
Kamihara Yasuhiro
Henry Jon
Olympus Optical Co,. Ltd.
Pillsbury & Winthrop LLP
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