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Experimental confirmation of non-scanning fluorescence confocal microscopy using speckle illumination
Optics Communications 238 (2004) 1–12 www.elsevier.com/locate/optcom
Experimental confirmation of non-scanning fluorescence confocal microscopy using speckle illumination q Shi-hong Jiang *, John G. Walker School of Electrical and Electronic Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK Received 27 January 2004; received in revised form 6 April 2004; accepted 26 April 2004
Abstract A novel non-scanning fluorescence confocal microscope arrangement that uses speckle illumination is described. The arrangement gives a full-field image without the need for a scanning system but requires averaging over a large number of independent frames. A method to reduce the number of frames to give an image of acceptable quality is investigated and computer simulation results are presented that demonstrate the effectiveness of this method. Experimental results are presented that show the confocal properties of depth discrimination and improved spatial resolution. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Confocal microscopy; Fluorescence; Speckle
1. Introduction Confocal fluorescence microscopy is an established technique in the biological sciences. It provides a valuable depth discrimination property that allows sliced images to be displayed and reduces the effect of flare or scattered light contributing to the image. Most instruments work on a scanning basis with the time and complexity of the scanning process being the main disadvantages of q
Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.optcom.2004.04.035. * Corresponding author. Tel.: +44-115-9515386; fax: +44115-9515616. E-mail addresses: [email protected] (S.-h. Jiang), [email protected] (J.G. Walker).
confocal systems compared with conventional microscopy. An early solution to the scan time problem was the tandem scanning system designed by Petran et al. [1]. This arrangement has not been adopted widely due to its inherent inefficiency in light gathering. Orthogonal coding and ‘structured light’ methods have been applied and implemented with more success [2,3]. Recently, a novel nonscanning fluorescence confocal microscopy using laser speckle illumination was proposed [4]. It uses a random time varying speckle pattern to illuminate the specimen, recording a sequence of widefield fluorescence images Iim and a sequence of corresponding speckle illumination patterns S. These recorded images are then processed by the averaging formula
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.04.035
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S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
Ip ðx; y; zÞ ¼ hIim ðx; y; zÞSðx; y; zÞi hIim ðx; y; zÞihSðx; y; zÞi:
Fig. 1. Simulated images of a uniform fluorescent object. For comparison purposes, the first column shows sets of images of the object at a number of focal positions generated using the calculated response from a conventional microscope. The second column shows the images using the calculated response from a fluorescence scanning confocal microscope. The third to sixth columns show a series of simulated images of the same object calculated using Eq. (1), but averaged over 500, 1000, 1500 and 2000 independent frames, respectively. The images are shown for the in-focus case (top row) and for the object defocused by 0.5, 1, 1.5 and 2 lm, respectively (rows two to five).
ð1Þ
It was shown in [4] that the processed image Ip would be equivalent to a confocal (type-2) image with enhanced lateral resolution and depth discrimination if an infinitive ensemble of frames were used. Of course, in reality only a finite number of frames may be used and this results in unwanted intensity variations in the processed image. In this paper, methods are investigated to reduce the number of frames required for an image of acceptable visual quality. A number of quantitative performance evaluations of the imaging performance are given including the depth discrimination property, lateral resolution and, in particular, intensity non-uniformity and non-linearity. An experimental system designed to verify the proposed arrangement is described. Images of a field of 4 lm diameter fluorescent microspheres in type 1 and type 2 modes obtained with an objective of NA ¼ 0.12 at 488 nm excitation radiation
1 scanning, theoretical non-scanning, 1000 averages 0.9
0.8
〈I(u)〉/〈I(0)〉
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
10
optical unit u
Fig. 2. Comparison of depth discrimination property between scanning and non-scanning fluorescence confocal microscopes.
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
are presented. The type 2 images show an evident depth discrimination property and enhanced lateral resolution.
3
form planar object to the in-focus integrated intensity Iint ð0Þ [5] Iint ðuÞ=Iint ð0Þ;
ð2Þ 2
2. System performance evaluation In this section four important aspects of confocal system performance are examined. These are: the depth discrimination property, the image intensity uniformity, the full-width at half-maximum intensity (FWHM) of the point spread function (PSF) and the non-linear variation of image intensity with fluorescence radiation.
where the optical unit u ¼ 2pDzN =k1 , Dz is the defocus distance, N is the numerical aperture, k1 is the wavelength of illumination light. Results of a simulation for a uniform object, with N ¼ 0:5, k1 ¼ 0:5 lm and the fluorescent wave length k2 ¼ 0:6 lm, are given in Fig. 1. Fig. 2 shows the depth discrimination property calculated with (2) using the data from the images of Fig. 1. It may be seen that the scanning and non-scanning confocal microscopes have indistinguishable responses to defocus.
2.1. Depth discrimination 2.2. Intensity non-uniformity The depth discrimination property can be evaluated in terms of the ratio of the out-of-focus integrated intensity Iint ðuÞ in the image of a uni-
In Fig. 1, unwanted intensity variations in the images of non-scanning confocal arrangement
0.16 without A-law processing 0.14
with A-law processing, A=10, V=10 〈S〉 with A-law processing, A=20, V=10 〈S〉
0.12
σ
0.1
0.08
0.06
0.04
0.02
0
500
1000
1500
2000
number of averaging Fig. 3. Intensity non-uniformity (r) for a non-scanning confocal arrangement for averaging over a varying number of frames. The solid line is for processing according to Eq. (1). The dashed and dotted lines are for processing using the logarithmic processing described in Section 3, for the case of A ¼ 10 and for A ¼ 20, respectively.
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S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
Fig. 4. Simulated image of nine isolated point sources in a non-scanning confocal microscope.
0.45 scanning confocal 0.44 non-scanning, 1000 averages
FWHM (µm)
0.43
0.42
0.41
0.4
0.39
0.38
0
0.5
1
1.5
2
defocus distance z (µm)
Fig. 5. Average FWHM of the nine peaks in the simulated image of a scanning and non-scanning confocal microscope. The error bars indicate the SD.
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
are evident and it may be noted that this nonuniformity decreases slowly as the number of frames increases. A suitable evaluation criterion for this intensity non-uniformity may be expressed as
r¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 hI 2 i hIi hIi
;
5
ð3Þ
where I denotes the intensity in the image. For a scanning confocal microscope, r should approach
Fig. 6. Image of a test object consisting of nine isolated points with fluorescence radiation level varying from 1 to 9 level in a nonscanning confocal microscope: (a) in focus, (b) 2 lm out of focus.
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zero. A plot of r against the number of averaging frames is shown in Fig. 3. It may be noted that, as expected, r decreases with the square root of the number of frames. 2.3. Lateral resolution
2.4. Non-linear variation of image intensity A further criterion to judge the output of a microscope arrangement is whether the final image intensity varies linearly with the strength of the fluorescence. To investigate this, a test object consisting of nine isolated points with fluorescence
Fig. 4 shows a simulated image of nine isolated point sources with equal fluorescence emission in a non-scanning microscope. Since the peaks in Fig. 4 are slightly different from each other in height due to the non-uniformity phenomenon discussed in Section 2.2, results are presented in Fig. 5 for the FWHM averaged over the nine peaks together with error bars based on the standard deviation of the nine measured FWHMs. It may be seen that the results for the non-scanning arrangement are very similar to those for the scanning microscope.
Im
I V/A
V
Fig. 8. The A-Law compression characteristic.
0.05 scanning confocal non-scanning, 1000 averages 0.04
in focus
energy
0.03
0.02
2 µm out of focus 0.01
0
1
2
3
4
5
6
7
8
9
peak number Fig. 7. Plot of the energy in the peaks of Fig. 6, together with the corresponding results for a scanning confocal system.
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
radiation level varying from 1 to 9 was used. Two sample simulated images are shown in Fig. 6. Nonlinearity is tested by comparing the energy
7
contained in each peak against the fluorescent radiation level in the corresponding point source. Fig. 7 shows the energy in the peaks of Fig. 6, together with the corresponding results for a scanning confocal system. It may be noted that the non-scanning arrangement gives good linearity.
3. Non-linear processing
Fig. 9. Simulated images of a uniform fluorescent object with A-Law processing applied to speckle patterns.
It is well known that the intensity distribution in a laser speckle pattern obeys a negative-exponential probability density function [6]. This distribution has a high probability of low intensities and a lower probability of higher intensities. This wide variation in intensity levels has the effect of lowering the efficiency of the averaging process in Eq. (1) and accounts for the large number of frames required to get a reasonable value for image uniformity illustrated in Fig. 3.
〈I (u) 〉/〈I (0) 〉
scanning, theoretical non-scanning, A-law processing 1000 averages
Fig. 10. Comparison of depth discrimination property between scanning and non-scanning with A-Law processing applied to speckle patterns.
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In this section, the results of applying a type of compression to the speckle intensities are presented. The compression characteristic selected is one commonly used in telephone systems known as the A-Law characteristic [7]. The input intensity is divided into three regions and the output modified intensity Im is given by 8 AI for 0 6 I 6 VA ðlinearÞ; < 1þln A V ð1þlnðAI=V ÞÞ Im ¼ for VA 6 I 6 V ðlogarithmicÞ; : 1þln A V for I > V ðlimitedÞ; ð4Þ where V is the maximum value of the detected intensity and A is the compression coefficient. The characteristic is shown in Fig. 8. Applying A-Law processing to each individual speckle pattern before the averaging process (1), new simulation results are obtained and these are shown in Fig. 9. Compared with Fig. 1, it may be
seen that the image uniformity for a given number of frames is significantly improved. Or, conversely, for a given image quality the number of frames can be reduced by about 50%. A comparison of the image uniformity parameter r for the cases with and without A-Law processing is shown in Fig. 3. where S is the mean intensity of We set V ¼ 10S, speckle pattern, as in this case the probability of speckle intensity larger than V is just ¼ expð10Þ 0:00005. expðV =SÞ This result is very encouraging in terms of reducing the time to acquire a non-scanning image in a reasonable time. However, this approach will only be useful if this non-linear processing does not adversely affect the other performance criteria considered in Section 2. Fig. 10 shows a comparison of the depth discrimination performance of the non-scanning arrangement using A-Law processing and the conventional scanning system. Fig. 11 shows a comparison of the average reso-
0.45 scanning confocal 0.44
non-scanning with A-law processing 1000 averages
FWHM (µm)
0.43
0.42
0.41
0.4
0.39
0.38
0
0.5
1
1.5
2
defocus distance z (µm) Fig. 11. Average FWHM of the nine peaks in the simulated image of a non-scanning confocal microscope with A-Law processing. The error bars indicate the SD.
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
9
0.05
scanning confocal non-scanning with A-law processing, 1000 averages
0.04
energy
0.03 in focus
0.02
2 µm out of focus 0.01
0
1
2
3
4
5
6
7
8
9
peak number Fig. 12. Plot of energy against the peak number for the case of A-Law processing.
lution measure FWHM obtained in conventional scanning and with the A-Law processed nonscanning system. Only a marginal reduction in the depth discrimination performance and lateral resolution is observed. Fig. 12 shows a comparison of the linearity of the A-Law and scanning arrangements. No significant decrease in linearity is observed using the A-Law processing.
4. Experimental results and discussion Encouraged by the results of the computer simulations presented in Section 3, a prototype optical bench system was constructed to demonstrate the practicality of the system. A diagram of the experimental arrangement is shown in Fig. 13. Illumination is from a solid-state diode-pumped laser beam passed through a ground-glass disc, a collimating lens and an objective. The dichroic beamsplitter directs the beam to form a speckle pattern
throughout the specimen region. The fluorescent light from the specimen at a longer wavelength is imaged via the lenses and the beam-splitter onto the CCD camera. In this system, the fluorescence images and their corresponding illumination speckle patterns are recorded separately. This requires that the diffuser ‘‘remember’’ all the positions in a duty cycle and generate precisely the same sequence of speckle patterns repetitively. A stepper motor is used for this purpose. At every diffuser position, the camera takes a frame. A filter centred on the emission wavelength is used for blocking unwanted laser light in the fluorescence image recording session. In the speckle pattern recording session, the dichroic beam-splitter is replaced with a mirror turned by 90° and a diaphragm is added to generate the correct speckle size. The principal parameters for the experiment are listed in Table 1. The type 1 images are obtained by taking an average over 500 individual fluorescence images (see Movie 1) each illuminated with a
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S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12 mirror dichroic beamsplitter diaphragm specimen CCD camera
filter at fluorescent light
tube lens
objective collimating lens
diffuser
computer
stepper motor
attenuator laser
Fig. 13. A schematic diagram of the experimental arrangement. Dotted components: used in the speckle pattern recording session. Dashed components: used in the fluorescence image recording session. Solid components: used in both sessions.
Table 1 Principal parameters for the experiment k1 ¼ 488 nm k2 ¼ 520 nm NA ¼ 0.12 r ¼ 0:61k2 =NA ¼ 2:64 lm f1 ¼ 25:5 mm 2f1 NA ¼ 6.12 mm f2 ¼ 500 mm 430 lm 340 lm 640 512 pixels 0.72° 500
Wavelength of laser light Wavelength of fluorescence light Numerical aperture of the objective Rayleigh resolution distance Focal length of the objective Aperture diameter of the diaphragm Focal length of the tube lens Field of view CCD resolution Angular movement of the diffuser Number of steps per revolution for the diffuser
different speckle pattern (see Movie 2). A series of such images of 4 lm fluorescent microspheres [8] at focal positions of 0, 20, 40 and 60 lm are shown in Figs. 14(a)–(d), respectively. The non-scanning, or type 2, images at the same focal positions computed using Eq. (1) and averaging over 500 frames are shown in Figs. 14(e)–(h), giving evident depth discrimination property and reduced effect of flare. The type 2 images with A-Law processing applied to speckle patterns (see Movie 3) are shown in Figs. 14(i)–(l) with the same response to defocus. Surface and profile plots of the local regions illustrated in Figs. 14(a), (e) and (i) are shown in Figs. 15(a)–(c), respectively. It may be seen that the rightmost double bead can hardly be
resolved for the type 1 case, but is clearly resolved for the type 2 case. For the A-Law processing case not only is it clearly resolved, but the intensity distribution is less distorted, as the intensity nonlinearity in the image has been reduced.
5. Conclusions A method to reduce the intensity variations in a speckle-illuminated non-scanning confocal microscope arrangement has been described. It has been shown through computer simulations that this method does not significantly change the resolution, depth discrimination or linearity of the sys-
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
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Fig. 14. Images of 4 lm fluorescent microspheres (640 512 12) at focal positions of 0, 20, 40 and 60 lm: (a)–(d) type 1 images; (e)–(h) type 2 images; (i)–(l) type 2 with A-Law processing (A ¼ 10, V ¼ 4095).
tem. Experimental results have demonstrated the practicality of one optical setup that implements non-scanning arrangement without the complexity of a raster scan. The experimentally obtained im-
ages of 4 lm diameter standard fluorescent calibration spheres with 500 averages exhibit excellent agreement with theory, and show the improved performance predicted by computer simulation. It
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Fig. 15. Surface and profile plots of local regions: (a) type 1 case; (b) type 2 case; (c) type 2 with A-Law processing.
should be noted however that the setup used here is aimed at demonstration of principle, the use of a stepper motor and separate recording of the speckle frames and the fluorescent frames would be slower than conventional scanning systems. Work towards a system with a reduced data collection time is ongoing. Acknowledgements Shi-hong Jiang is grateful for support from the International Office of the University of Nottingham.
References [1] M. Petran, M. Hadravsky, M.D. Egger, R. Galambos, J. Opt. Soc. Am. 58 (1968) 661. [2] M.A.A. Neil, A. Squire, R. Juskaitis, P.I.H. Bastiaens, T. Wilson, J. Microsc. 197 (2000) 1. [3] D. Karadaglic, R. Juskaitis, T. Wilson, Scanning 24 (2002) 310. [4] J.G. Walker, Opt. Commun. 189 (2001) 221. [5] T. Wilson, Confocal Microscopy, Academic Press, San Diego, CA, 1990. [6] J.W. Goodman, Statistical Optics, Wiley, New York, 1985. [7] J. Dunlop, D.G. Smith, Telecommunications Engineering, Chapman & Hall, London, 1994. [8] Microsheres supplied by Molecular Probes Ltd, Eugene, OR.
Experimental confirmation of non-scanning fluorescence confocal microscopy using speckle illumination q Shi-hong Jiang *, John G. Walker School of Electrical and Electronic Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK Received 27 January 2004; received in revised form 6 April 2004; accepted 26 April 2004
Abstract A novel non-scanning fluorescence confocal microscope arrangement that uses speckle illumination is described. The arrangement gives a full-field image without the need for a scanning system but requires averaging over a large number of independent frames. A method to reduce the number of frames to give an image of acceptable quality is investigated and computer simulation results are presented that demonstrate the effectiveness of this method. Experimental results are presented that show the confocal properties of depth discrimination and improved spatial resolution. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Confocal microscopy; Fluorescence; Speckle
1. Introduction Confocal fluorescence microscopy is an established technique in the biological sciences. It provides a valuable depth discrimination property that allows sliced images to be displayed and reduces the effect of flare or scattered light contributing to the image. Most instruments work on a scanning basis with the time and complexity of the scanning process being the main disadvantages of q
Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.optcom.2004.04.035. * Corresponding author. Tel.: +44-115-9515386; fax: +44115-9515616. E-mail addresses: [email protected] (S.-h. Jiang), [email protected] (J.G. Walker).
confocal systems compared with conventional microscopy. An early solution to the scan time problem was the tandem scanning system designed by Petran et al. [1]. This arrangement has not been adopted widely due to its inherent inefficiency in light gathering. Orthogonal coding and ‘structured light’ methods have been applied and implemented with more success [2,3]. Recently, a novel nonscanning fluorescence confocal microscopy using laser speckle illumination was proposed [4]. It uses a random time varying speckle pattern to illuminate the specimen, recording a sequence of widefield fluorescence images Iim and a sequence of corresponding speckle illumination patterns S. These recorded images are then processed by the averaging formula
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.04.035
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S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
Ip ðx; y; zÞ ¼ hIim ðx; y; zÞSðx; y; zÞi hIim ðx; y; zÞihSðx; y; zÞi:
Fig. 1. Simulated images of a uniform fluorescent object. For comparison purposes, the first column shows sets of images of the object at a number of focal positions generated using the calculated response from a conventional microscope. The second column shows the images using the calculated response from a fluorescence scanning confocal microscope. The third to sixth columns show a series of simulated images of the same object calculated using Eq. (1), but averaged over 500, 1000, 1500 and 2000 independent frames, respectively. The images are shown for the in-focus case (top row) and for the object defocused by 0.5, 1, 1.5 and 2 lm, respectively (rows two to five).
ð1Þ
It was shown in [4] that the processed image Ip would be equivalent to a confocal (type-2) image with enhanced lateral resolution and depth discrimination if an infinitive ensemble of frames were used. Of course, in reality only a finite number of frames may be used and this results in unwanted intensity variations in the processed image. In this paper, methods are investigated to reduce the number of frames required for an image of acceptable visual quality. A number of quantitative performance evaluations of the imaging performance are given including the depth discrimination property, lateral resolution and, in particular, intensity non-uniformity and non-linearity. An experimental system designed to verify the proposed arrangement is described. Images of a field of 4 lm diameter fluorescent microspheres in type 1 and type 2 modes obtained with an objective of NA ¼ 0.12 at 488 nm excitation radiation
1 scanning, theoretical non-scanning, 1000 averages 0.9
0.8
〈I(u)〉/〈I(0)〉
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
10
optical unit u
Fig. 2. Comparison of depth discrimination property between scanning and non-scanning fluorescence confocal microscopes.
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
are presented. The type 2 images show an evident depth discrimination property and enhanced lateral resolution.
3
form planar object to the in-focus integrated intensity Iint ð0Þ [5] Iint ðuÞ=Iint ð0Þ;
ð2Þ 2
2. System performance evaluation In this section four important aspects of confocal system performance are examined. These are: the depth discrimination property, the image intensity uniformity, the full-width at half-maximum intensity (FWHM) of the point spread function (PSF) and the non-linear variation of image intensity with fluorescence radiation.
where the optical unit u ¼ 2pDzN =k1 , Dz is the defocus distance, N is the numerical aperture, k1 is the wavelength of illumination light. Results of a simulation for a uniform object, with N ¼ 0:5, k1 ¼ 0:5 lm and the fluorescent wave length k2 ¼ 0:6 lm, are given in Fig. 1. Fig. 2 shows the depth discrimination property calculated with (2) using the data from the images of Fig. 1. It may be seen that the scanning and non-scanning confocal microscopes have indistinguishable responses to defocus.
2.1. Depth discrimination 2.2. Intensity non-uniformity The depth discrimination property can be evaluated in terms of the ratio of the out-of-focus integrated intensity Iint ðuÞ in the image of a uni-
In Fig. 1, unwanted intensity variations in the images of non-scanning confocal arrangement
0.16 without A-law processing 0.14
with A-law processing, A=10, V=10 〈S〉 with A-law processing, A=20, V=10 〈S〉
0.12
σ
0.1
0.08
0.06
0.04
0.02
0
500
1000
1500
2000
number of averaging Fig. 3. Intensity non-uniformity (r) for a non-scanning confocal arrangement for averaging over a varying number of frames. The solid line is for processing according to Eq. (1). The dashed and dotted lines are for processing using the logarithmic processing described in Section 3, for the case of A ¼ 10 and for A ¼ 20, respectively.
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S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
Fig. 4. Simulated image of nine isolated point sources in a non-scanning confocal microscope.
0.45 scanning confocal 0.44 non-scanning, 1000 averages
FWHM (µm)
0.43
0.42
0.41
0.4
0.39
0.38
0
0.5
1
1.5
2
defocus distance z (µm)
Fig. 5. Average FWHM of the nine peaks in the simulated image of a scanning and non-scanning confocal microscope. The error bars indicate the SD.
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
are evident and it may be noted that this nonuniformity decreases slowly as the number of frames increases. A suitable evaluation criterion for this intensity non-uniformity may be expressed as
r¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 hI 2 i hIi hIi
;
5
ð3Þ
where I denotes the intensity in the image. For a scanning confocal microscope, r should approach
Fig. 6. Image of a test object consisting of nine isolated points with fluorescence radiation level varying from 1 to 9 level in a nonscanning confocal microscope: (a) in focus, (b) 2 lm out of focus.
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S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
zero. A plot of r against the number of averaging frames is shown in Fig. 3. It may be noted that, as expected, r decreases with the square root of the number of frames. 2.3. Lateral resolution
2.4. Non-linear variation of image intensity A further criterion to judge the output of a microscope arrangement is whether the final image intensity varies linearly with the strength of the fluorescence. To investigate this, a test object consisting of nine isolated points with fluorescence
Fig. 4 shows a simulated image of nine isolated point sources with equal fluorescence emission in a non-scanning microscope. Since the peaks in Fig. 4 are slightly different from each other in height due to the non-uniformity phenomenon discussed in Section 2.2, results are presented in Fig. 5 for the FWHM averaged over the nine peaks together with error bars based on the standard deviation of the nine measured FWHMs. It may be seen that the results for the non-scanning arrangement are very similar to those for the scanning microscope.
Im
I V/A
V
Fig. 8. The A-Law compression characteristic.
0.05 scanning confocal non-scanning, 1000 averages 0.04
in focus
energy
0.03
0.02
2 µm out of focus 0.01
0
1
2
3
4
5
6
7
8
9
peak number Fig. 7. Plot of the energy in the peaks of Fig. 6, together with the corresponding results for a scanning confocal system.
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
radiation level varying from 1 to 9 was used. Two sample simulated images are shown in Fig. 6. Nonlinearity is tested by comparing the energy
7
contained in each peak against the fluorescent radiation level in the corresponding point source. Fig. 7 shows the energy in the peaks of Fig. 6, together with the corresponding results for a scanning confocal system. It may be noted that the non-scanning arrangement gives good linearity.
3. Non-linear processing
Fig. 9. Simulated images of a uniform fluorescent object with A-Law processing applied to speckle patterns.
It is well known that the intensity distribution in a laser speckle pattern obeys a negative-exponential probability density function [6]. This distribution has a high probability of low intensities and a lower probability of higher intensities. This wide variation in intensity levels has the effect of lowering the efficiency of the averaging process in Eq. (1) and accounts for the large number of frames required to get a reasonable value for image uniformity illustrated in Fig. 3.
〈I (u) 〉/〈I (0) 〉
scanning, theoretical non-scanning, A-law processing 1000 averages
Fig. 10. Comparison of depth discrimination property between scanning and non-scanning with A-Law processing applied to speckle patterns.
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In this section, the results of applying a type of compression to the speckle intensities are presented. The compression characteristic selected is one commonly used in telephone systems known as the A-Law characteristic [7]. The input intensity is divided into three regions and the output modified intensity Im is given by 8 AI for 0 6 I 6 VA ðlinearÞ; < 1þln A V ð1þlnðAI=V ÞÞ Im ¼ for VA 6 I 6 V ðlogarithmicÞ; : 1þln A V for I > V ðlimitedÞ; ð4Þ where V is the maximum value of the detected intensity and A is the compression coefficient. The characteristic is shown in Fig. 8. Applying A-Law processing to each individual speckle pattern before the averaging process (1), new simulation results are obtained and these are shown in Fig. 9. Compared with Fig. 1, it may be
seen that the image uniformity for a given number of frames is significantly improved. Or, conversely, for a given image quality the number of frames can be reduced by about 50%. A comparison of the image uniformity parameter r for the cases with and without A-Law processing is shown in Fig. 3. where S is the mean intensity of We set V ¼ 10S, speckle pattern, as in this case the probability of speckle intensity larger than V is just ¼ expð10Þ 0:00005. expðV =SÞ This result is very encouraging in terms of reducing the time to acquire a non-scanning image in a reasonable time. However, this approach will only be useful if this non-linear processing does not adversely affect the other performance criteria considered in Section 2. Fig. 10 shows a comparison of the depth discrimination performance of the non-scanning arrangement using A-Law processing and the conventional scanning system. Fig. 11 shows a comparison of the average reso-
0.45 scanning confocal 0.44
non-scanning with A-law processing 1000 averages
FWHM (µm)
0.43
0.42
0.41
0.4
0.39
0.38
0
0.5
1
1.5
2
defocus distance z (µm) Fig. 11. Average FWHM of the nine peaks in the simulated image of a non-scanning confocal microscope with A-Law processing. The error bars indicate the SD.
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
9
0.05
scanning confocal non-scanning with A-law processing, 1000 averages
0.04
energy
0.03 in focus
0.02
2 µm out of focus 0.01
0
1
2
3
4
5
6
7
8
9
peak number Fig. 12. Plot of energy against the peak number for the case of A-Law processing.
lution measure FWHM obtained in conventional scanning and with the A-Law processed nonscanning system. Only a marginal reduction in the depth discrimination performance and lateral resolution is observed. Fig. 12 shows a comparison of the linearity of the A-Law and scanning arrangements. No significant decrease in linearity is observed using the A-Law processing.
4. Experimental results and discussion Encouraged by the results of the computer simulations presented in Section 3, a prototype optical bench system was constructed to demonstrate the practicality of the system. A diagram of the experimental arrangement is shown in Fig. 13. Illumination is from a solid-state diode-pumped laser beam passed through a ground-glass disc, a collimating lens and an objective. The dichroic beamsplitter directs the beam to form a speckle pattern
throughout the specimen region. The fluorescent light from the specimen at a longer wavelength is imaged via the lenses and the beam-splitter onto the CCD camera. In this system, the fluorescence images and their corresponding illumination speckle patterns are recorded separately. This requires that the diffuser ‘‘remember’’ all the positions in a duty cycle and generate precisely the same sequence of speckle patterns repetitively. A stepper motor is used for this purpose. At every diffuser position, the camera takes a frame. A filter centred on the emission wavelength is used for blocking unwanted laser light in the fluorescence image recording session. In the speckle pattern recording session, the dichroic beam-splitter is replaced with a mirror turned by 90° and a diaphragm is added to generate the correct speckle size. The principal parameters for the experiment are listed in Table 1. The type 1 images are obtained by taking an average over 500 individual fluorescence images (see Movie 1) each illuminated with a
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S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12 mirror dichroic beamsplitter diaphragm specimen CCD camera
filter at fluorescent light
tube lens
objective collimating lens
diffuser
computer
stepper motor
attenuator laser
Fig. 13. A schematic diagram of the experimental arrangement. Dotted components: used in the speckle pattern recording session. Dashed components: used in the fluorescence image recording session. Solid components: used in both sessions.
Table 1 Principal parameters for the experiment k1 ¼ 488 nm k2 ¼ 520 nm NA ¼ 0.12 r ¼ 0:61k2 =NA ¼ 2:64 lm f1 ¼ 25:5 mm 2f1 NA ¼ 6.12 mm f2 ¼ 500 mm 430 lm 340 lm 640 512 pixels 0.72° 500
Wavelength of laser light Wavelength of fluorescence light Numerical aperture of the objective Rayleigh resolution distance Focal length of the objective Aperture diameter of the diaphragm Focal length of the tube lens Field of view CCD resolution Angular movement of the diffuser Number of steps per revolution for the diffuser
different speckle pattern (see Movie 2). A series of such images of 4 lm fluorescent microspheres [8] at focal positions of 0, 20, 40 and 60 lm are shown in Figs. 14(a)–(d), respectively. The non-scanning, or type 2, images at the same focal positions computed using Eq. (1) and averaging over 500 frames are shown in Figs. 14(e)–(h), giving evident depth discrimination property and reduced effect of flare. The type 2 images with A-Law processing applied to speckle patterns (see Movie 3) are shown in Figs. 14(i)–(l) with the same response to defocus. Surface and profile plots of the local regions illustrated in Figs. 14(a), (e) and (i) are shown in Figs. 15(a)–(c), respectively. It may be seen that the rightmost double bead can hardly be
resolved for the type 1 case, but is clearly resolved for the type 2 case. For the A-Law processing case not only is it clearly resolved, but the intensity distribution is less distorted, as the intensity nonlinearity in the image has been reduced.
5. Conclusions A method to reduce the intensity variations in a speckle-illuminated non-scanning confocal microscope arrangement has been described. It has been shown through computer simulations that this method does not significantly change the resolution, depth discrimination or linearity of the sys-
S.-h. Jiang, J.G. Walker / Optics Communications 238 (2004) 1–12
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Fig. 14. Images of 4 lm fluorescent microspheres (640 512 12) at focal positions of 0, 20, 40 and 60 lm: (a)–(d) type 1 images; (e)–(h) type 2 images; (i)–(l) type 2 with A-Law processing (A ¼ 10, V ¼ 4095).
tem. Experimental results have demonstrated the practicality of one optical setup that implements non-scanning arrangement without the complexity of a raster scan. The experimentally obtained im-
ages of 4 lm diameter standard fluorescent calibration spheres with 500 averages exhibit excellent agreement with theory, and show the improved performance predicted by computer simulation. It
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Fig. 15. Surface and profile plots of local regions: (a) type 1 case; (b) type 2 case; (c) type 2 with A-Law processing.
should be noted however that the setup used here is aimed at demonstration of principle, the use of a stepper motor and separate recording of the speckle frames and the fluorescent frames would be slower than conventional scanning systems. Work towards a system with a reduced data collection time is ongoing. Acknowledgements Shi-hong Jiang is grateful for support from the International Office of the University of Nottingham.
References [1] M. Petran, M. Hadravsky, M.D. Egger, R. Galambos, J. Opt. Soc. Am. 58 (1968) 661. [2] M.A.A. Neil, A. Squire, R. Juskaitis, P.I.H. Bastiaens, T. Wilson, J. Microsc. 197 (2000) 1. [3] D. Karadaglic, R. Juskaitis, T. Wilson, Scanning 24 (2002) 310. [4] J.G. Walker, Opt. Commun. 189 (2001) 221. [5] T. Wilson, Confocal Microscopy, Academic Press, San Diego, CA, 1990. [6] J.W. Goodman, Statistical Optics, Wiley, New York, 1985. [7] J. Dunlop, D.G. Smith, Telecommunications Engineering, Chapman & Hall, London, 1994. [8] Microsheres supplied by Molecular Probes Ltd, Eugene, OR.