Method and device for reconstructing images

1. A method for reconstruction of an image function (r), which represents an object function (ƒ) of an object ( 1 ) imaged with periodically structured illumination, from optical section images (g c , g s ) which are formed after convolution operations on the object function (ƒ) with a modified illumination point spread function (h I ), said method comprising:

generation of corrected optical section images (g c ′, g s ′), wherein predetermined filter operators that are the inverse of the convolution operations are applied on the optical section images (g c , g s ), and

demodulation (S 2 ) of the corrected optical section images (g c ′, g s ′) in order to generate the image function (r).

2. The method according to claim 1 wherein the filter operators comprise linear, regularized inverse filter operators.

3. The method according to claim 1 , wherein the filter operators are constructed from Fourier transforms of the optical section images (g c , g s ) and the modified illumination point spread function (h I ).

4. The method according to claim 1 , wherein the optical section images (g c , g s ) are formed after convolution operations defined by

g c ( x )=(ƒ( x )cos(ω x ))*( v ( z )| h D ( x )| 2 ) and

g s ( x )=−(ƒ( x )sin(ω x ))*( v ( z )| h D ( x )| 2 )

wherein (h D ) is a detection point spread function and v(z)=∫cos(ωx 1 )[∫|h I (x 1 , y 1 , z)| 2 dy 1 ]dx 1 .

5. The method according to claim 4 , wherein the corrected optical section images (g c ′, g s ′) are calculated with filter operators defined by:

g

c

′

=

f

⁢

⁢

cos

⁡

(

ω

⁢

⁢

x

)

=

F

-

1

⁢

{

H

D

*

G

C



H

D



2

+

β

}

⁢

⁢

and

g

s

′

=

f

⁢

⁢

sin

⁡

(

ω

⁢

⁢

x

)

=

-

F

-

1

⁢

{

H

D

*

G

S



H

D



2

+

β

}

,

where

H D =F{v|h D | 2 }, G C =F{g c }, G S =F{g s }, wherein β is a predetermined regularization parameter.

6. The method according to claim 5 , comprising the step:

setting the regularization parameter β depending on at least one property of the optical section images (g c , g s ).

7. The method according to claim 6 , wherein the regularization parameter β is set depending on a noise parameter of the optical section images (g c , g s ).

8. The method according to claim 1 , wherein, for demodulation of the corrected optical section images (g c ′, g s ′), the image function (r) is calculated according to r=√{square root over (g′ c 2 +g′ s 2 )}.

9. The method according to claim 1 , wherein, for demodulation of the corrected optical section images (g c ′, g s ′), the image function (r) is calculated according to r=└g c ′+jg s ′┘e jωx .

10. The method according to claim 1 , wherein the optical section images (g c , g s ) are formed immediately following recording of an image.

11. The method according to claim 1 , wherein the optical section images (g c , g s ) are determined by reverse modulation from an uncorrected image function (r′).

12. An imaging method for obtaining an image function (r) of an object, comprising the steps:

periodically structured illumination of the object ( 1 ),

detection of a plurality of intermediate images (g′),

determination of optical section images (g c , g s ) from the intermediate images (g i ), and

reconstruction of the image function (r) with a method according to claim 1 .

13. An imaging apparatus for obtaining an image function (r) of an object, which comprises:

an image recording device for periodically structured illumination of the object and for detection of a plurality of intermediate images (g′),

a section image calculator for determining optical section images (g c , g s ) from the intermediate images (g i ), and

a reconstruction device for reconstructing an image function (r) which represents an object function (ƒ) of the object, from the optical section images (g c , g s ), wherein the reconstruction device comprises a filter circuit for applying predetermined filter operations on the optical section images (g c , g s ) in order to generate corrected optical section images (g c ′, g s ′) and a demodulation circuit for generating the image function (r) from the corrected optical section images (g c ′, g s ′).

14. The imaging device according to claim 13 , wherein the reconstruction device is configured to carry out a reconstruction method according to claim 1 .

15. The imaging device according to claim 13 , wherein the filter circuit comprises an adjusting element for adjusting the regularization parameter β.

16. The imaging device according to claim 13 , wherein the image recording device is part of an optical microscope.

17. A microscope, which comprises an imaging apparatus according to claim 13 .

18. A reconstruction device for reconstruction of an image function (r), which represents an object function (ƒ) of an object, from optical section images (g c , g s ), comprising:

a filter circuit for applying predetermined filter operators on the optical section images (g c , g s ) in order to generate corrected optical section images (g c ′, g s ′), and

a demodulation circuit for generating the image function (r) from the corrected optical section images (g c ′, g s ′).

19. A microscope, which comprises a reconstruction device according to claim 18 .

20. A computer program product situated on a computer-readable storage medium and having a program code for carrying out a reconstruction method according to claim 1 .

21. A device which comprises a computer-readable storage medium which contains program instructions for carrying out a reconstruction method according to claim 1 .