Implementation of Good Clinical Laboratory Practice in an Immunology Basic Research Laboratory: The KEMRI-Wellcome Trust Research Laboratories Experience.
Objectives: Good Clinical Laboratory Practice (GCLP) is a standard that ensures quality and reliability of research data by adopting the principles of Good Laboratory Practice and Good Clinical Practice. Even though implementing a quality system in a basic research laboratory is still a contentious issue, it ensures that the research data are accurate, valid, and reliable. GCLP implementation requires proper documented procedures and safety precautions to achieve this objective.Methods: This article describes the Kenya Medical Research Institute (KEMRI)-Wellcome Trust Research Laboratories experience in the implementation of GCLP guidelines in a laboratory conducting basic research.Results: The laboratory managed to implement GCLP elements that could be applied to a basic research laboratory, such as standard operating procedures, equipment management, laboratory analytical plans, organization, and personnel. The laboratory achieved GCLP accreditation in October 2015.Conclusions: The methodology, suggestions, and comments that arose from our experience in implementing GCLP guidelines can be used by other laboratories to develop a quality system using GCLP guidelines to support medical research conducted to ensure the research data are reliable and can be easily reconstructed in other research settings.
Gumba, H., Musyoki, J., Mosobo, M., Lowe, B.


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Prof. John Doyle
Professor John Doyle is Director of the Institute for International Conflict Resolution and Reconstruction (IICRR) in Dublin City University, Ireland and Executive Dean of the Faculty of Humanities and Social Sciences. His research interests include comparative nationalist and ethnic conflict; Northern Ireland; conflict in South Asia; and Irish foreign policy. John has taken part in a number of studies of comparative peace processes, including two EU funded projects with colleagues in South Asia, which brought academics from India, Pakistan, Sri Lanka, Bangladesh and Afghanistan together for a series of workshops, in New Delhi, Brussels and at DCU, examining both European examples such as Northern Ireland and the Balkans and South Asian cases including Kashmir, Sri Lanka, Nepal, the Indian North East and Afghanistan. He has been a visiting professor in conflict resolution in India, at the Nelson Mandela Centre in Jamia Millia Islamia, New Delhi and in Pakistan, in the School of Social Sciences in Lahore University of Management Sciences (LUMS). John did his PhD in Queens University Belfast and worked in University College Dublin before moving to DCU.

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Analysis of the depth of field of integral imaging displays based on wave optics
Cheng-Gao Luo, Xiao Xiao, Manuel Martínez-Corral, Chih-Wei Chen, Bahram Javidi, and Qiong-Hua Wang
Cheng-Gao Luo,1 Xiao Xiao,2 Manuel Martínez-Corral,3 Chih-Wei Chen,4 Bahram Javidi,2 and Qiong-Hua Wang1,*
1School of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China
2Electrical and Computer Engineering Department, University of Connecticut, 371 Fairfield Rd, Unit 2157, Storrs, CT 06269-2157, USA
3Departmentof Optics, University of Valencia, 46100 Burjassot, Spain
4Department of Photonics & Institute of Electro-Optical Engineering, Display Institute, National Chiao Tung University, Hsinchu 30010, Taiwan
*Corresponding author: qhwang@scu.edu.cn
C Luo
X Xiao
M Martínez-Corral
C Chen
B Javidi
Q Wang
Cheng-Gao Luo, Xiao Xiao, Manuel Martínez-Corral, Chih-Wei Chen, Bahram Javidi, and Qiong-Hua Wang, "Analysis of the depth of field of integral imaging displays based on wave optics," Opt. Express 21, 31263-31273 (2013)
Analysis of the depth of field for integral imaging with consideration of facet braiding (AO)
Analysis on enhanced depth of field for integral imaging microscope (OE)
Real-time capturing and 3D visualization method based on integral imaging (OE)
Integral imaging
Wave propagation
Three-dimensional image processing (100.6890)
Image formation theory (110.2990)
Information theoretical analysis (110.3055)
Propagation (350.5500)
Original Manuscript: September 10, 2013
Revised Manuscript: December 4, 2013
Manuscript Accepted: December 5, 2013
2. Previous DOF calculation methods
3. DOF calculation methods based on wave optics
4. DOF calculation results based on wave optics
5. Experimental results
Equations (13)
In this paper, we analyze the depth of field (DOF) of integral imaging displays based on wave optics. With considering the diffraction effect, we analyze the intensity distribution of light with multiple micro-lenses and derive a DOF calculation formula for integral imaging display system. We study the variations of DOF values with different system parameters. Experimental results are provided to verify the accuracy of the theoretical analysis. The analyses and experimental results presented in this paper could be beneficial for better understanding and designing of integral imaging displays.
Integral imaging is a 3D technique that was proposed by Lippman in 1908 [1]. It can provide full-parallax and continuous-viewing 3D images and does not require any special glasses or coherent light, such as those used in multi-view auto-stereoscopic 3D display or holography [2–7]. Integral imaging has attracted extensive attention for its research and application in the area of 3D sensing and display [8–29].
However, integral imaging displays are affected by diffraction and aberration effects in both optical pickup and display processes. To eliminate the effects of diffraction and aberration in the optical pickup process, computer-generated integral imaging can be applied [30]. It can generate elemental images by using computer graphic techniques with the parameters of the virtual micro-lens array (MLA) without a real optical system. Because of its flexibility and diffraction-free feature, computer-generated integral imaging has been proposed in many fields such as entertainment and medical sciences et al.. In such cases, the deterioration factor in the pickup process can be ignored and only the display process should be considered when analyzing the viewing performance of the system. In this paper, we analyze the depth of field (DOF) using computer-generated integral imaging.
The main parameters used to evaluate the performance of the integral imaging display are DOF, viewing resolution, and viewing angle [31–36]. In this paper, we focus on the analysis of the DOF of integral imaging displays using wave optics. First, we analyze the number of correspondence pixels which are responsible for reconstructing the same image point in 3D space. Then, by analyzing the wave propagation and light intensity distribution with multiple micro-lenses, we perform the DOF calculation based on hyperbola fitting and the minimum angular resolution of human eyes. By taking into consideration of the diffraction effect and using the superposition of light intensity with multiple micro-lenses, we can obtain more accurate DOF calculation results compared to the previous methods for the integral imaging display. Experimental results are also given to verify the accuracy of the proposed method.
This paper is organized as follows. In section 2, we review two pre-existing DOF calculation methods based on geometrical optics and Gaussian beam distribution model [37,38]. In section 3, we propose a DOF calculation method using wave optics [39,40]. In sections 4, we calculate several groups of DOF values using our proposed method and analyze the variations of DOF with different system parameters. In section 5, the accuracy of the method is verified by comparing the experimental results of the proposed method with the previous researches. In section 6, we summarize the main achievements of this paper and conclude with future directions and outlook.
One of the most important parameters that set 3D displays apart from 2D displays is their DOF. To understand the DOF of integral imaging displays, Min et al. [37] performed an analysis using geometrical optics theory without considering the diffraction effect caused by MLA. Because the integrated image is out of focus when the image is located away from the central depth plane (CDP), DOF can be set as the distance between the rear and front marginal depth planes, where the ray-optical focusing error occurs due to the overlap of the image pixel:
(1)DOFGeom=2l2g×ppd,
where p and pd represent the pitch of the MLA and the pixel size of the display, respectively. Parameter g represents the gap between the display and the MLA, and l represents the conjugate distance defined by the Gauss lens law [41].
A DOF calculation method based on Gaussian beam distribution model was also proposed [38]. In that model, the light emanating from a single pixel on the display was considered as a Gaussian beam whose waist is located at the CDP. Taking into account the minimum angular resolution of human eyes (αe) [42], the DOF was obtained by calculating the locations of the rear and front marginal depth planes based on the Gaussian beam function:
(2)DOFGauss=2l4tan(αe/2)2d2p2g2+4pd2tan(αe/2)2l4−p2l2pd2|4tan(αe/2)2l2g−gp2|,
where d refers to the viewing distance between the observer and the CDP.
These DOF calculation methods are easy to use but suffer from low accuracy because they both neglect the diffraction effect and only take a single micro-lens into consideration. Even though the second method tries to approximate the actual light intensity distribution in the image space, the obtained Gaussian light beam functions are derived from the geometrical relationships of the integral imaging display. It results in the low accuracy of the DOF calculation results.
Here, we propose another approach for DOF calculation using wave-optics. First, we analyze the number of correspondence pixels which are responsible for reconstructing the same image point in 3D space. Then, by analyzing the wave propagation and light intensity distribution with multiple micro-lenses, we perform the DOF calculation based on hyperbola fitting and the minimum angular resolution of human eyes.
Note that for an integral imaging display the pixel size of the display device is a factor that strongly influences the DOF [37,38]. However, in our analysis, we regard the display pixels as ideal points for simplification. We only consider square micro-lenses in this paper, but it is not difficult to expand our proposed method to other micro-lens shapes. In addition, our studies are based on resolution priority integral imaging (RPII) displays [43] while the derivations of depth priority integral imaging (DPII) [43] displays are similar.
3.1 Number of correspondence pixels of the RPII display
For a RPII display, the correspondence pixels are located on different elemental images and imaged by their corresponding micro-lenses to reconstruct the same image point on the conjugate plane, as shown in Fig. 1.Suppose the MLA contains M × N micro-lenses, and the central micro-lens is denoted as the 0th micro-lens. To describe the light propagation in the image space, we set up a coordinate system xyz in which the z axis coincides with the optical axis of the 0th micro-lens. And the origin is located at the center of that lens. Also, a plane coordinate system x0y0 is utilized to describe the MLA plane (z = 0).
Fig. 1 Number of correspondence pixels to reconstruct image point A in the RPII display.
We take image point A located on the z axis for example. Assuming the wth elemental image is the critical one that contains the correspondence pixel for image point A, according to the geometric relationships, w is given by
(3)w=⌊f2|g−f|⌋,
where the symbol ⌊x⌋ denotes the greatest integer less than or equal to x, distance f and g are defined as the focal length and the gap between the display and the MLA, respectively.
The number of correspondence pixels (H × V) for image point A is given by
(4)H×V={(2w+1)×(2w+1)(2w+1)≤min(M,N)M×(2w+1)M≤(2w+1)≤N(2w+1)×NN≤(2w+1)≤MM×N(2w+1)≥max(M,N),
where functions min(M, N) and max(M, N) give the smaller and the larger values of M and N, respectively.
Among the H × V correspondence pixels on the display panel (xD,yD), as shown in Fig. 1, the coordinates of an arbitrary correspondence pixel D(xmnD,ymnD) can be expressed with the system parameters as
(5)(xmnD,ymnD)=(gfmp,gfnp),
where m = -w…-1, 0, 1...w and n = -w…-1, 0, 1…w are the indexes of micro-lens in the MLA corresponding to the correspondence pixel D(xmnD,ymnD).
3.2 Light intensity distribution of the RPII display
After obtaining the number of correspondence pixels, we will analyze the light intensity distribution in the image space of the RPII display.
For the RPII display shown in Fig. 2, the pupil function for the central micro-lens can be given as
Fig. 2 Light intensity distribution of the RPII display.
(6)P00(x0,y0)=rect(x0p,y0p)={1-p2≤x0≤p2,-p2≤y0≤p20otherwise.
The pupil function for other micro-lenses can be expressed as Pmn(x0,y0)= P00(x0−mp,y0−np).
Assuming that the corresponding pixel D(xmnD,ymnD) is a δ function (point source), the phase transformation of the corresponding micro-lens is given by
(7)tmn(x0,y0)=P00(x0−mp,y0−np)exp{−jk2f[(x0−mp)2+(y0−np)2]}.
For a single correspondence pixel D(xmnD,ymnD), we can obtain the light intensity distribution at an arbitrary point C(x, y, z) on a certain depth plane by using the paraxial approximation and the Fresnel diffraction theory, as given below:
(8)Imn(x,y;z)=|1λ¯2gz∫∫−∞+∞exp{jk2g[(x0−xmnD)2+(y0−ymnD)2]}×tmn(x0,y0)×exp{jk2z[(x−x0)2+(y−y0)2]}dx0dy0|2,
where λ¯ is the mean wavelength, k is the wave number and is given by k=2π/λ¯.
For multiple correspondence pixels, all the intensity distributions can be superimposed linearly. Therefore, the light intensity distribution of the RPII display can be expressed as
(9)I(x,y;z)=∑m=−w,n=−wm=w,n=wImn(x,y;z).
3.3 DOF of the RPII display
In the following parts, we only take into account one dimension for simplicity, and the discussions for the other dimension are the same due to the square shapes of micro-lenses.
For a given RPII display the diffraction intensity patterns on different depth planes can be obtained by using Eqs. (8) and (9). Figures 3(a) and 3(b) show the diffraction intensity patterns at depth planes z = 20.0mm (the conjugate plane) and z = 26.0mm with parameters f = 4.0mm, g = 5.0mm, p = 0.8mm, λ¯=5.5×10−4mm, and the number of correspondence pixels H × V = 5 × 5.
Fig. 3 Cross sections and meridian sections (y = 0) of the diffraction intensity patterns on different depth planes (a) z = 20.0mm and (b) z = 26.0mm. Here, f = 4.0mm, g = 5.0mm, p = 0.8mm, λ¯=5.5×10−4mm, and H × V = 5 × 5.
For different depth planes, the corresponding diffraction intensity patterns can be calculated as shown in Fig. 3. For a given diffraction intensity pattern, we use a square light spot that contains a substantial percentage (84%) of the whole pattern energy to replace the entire pattern [44]. The diffraction intensity pattern can then be simplified as a square light spot with a half side length r(z). Therefore, r(z) can be calculated as
(10)∫-r(z)r(z)I(x,0;z)dx=0.84∫-∞∞I(x,0;z)dx.
The discrete data of half side length r(z) is obtained and fitted into a hyperbola function whose waist is located on the conjugate plane, as denoted by the red lines in Fig. 4.Taking into consideration the minimum angular resolution of human eyes (αe), we can calculate the DOF using the intersection of the hyperbola and the margin lines of αe (blue lines shown in Fig. 4). Here, d represents the viewing distance between the eye and the conjugate plane.
Fig. 4 Analysis of DOF of the RPII display based on wave optics taking into account the minimum angular resolution of human eyes.
After obtaining the hyperbola functions, we can deduce the DOF as follows. The hyperbola fitting function of the light beam can be written as
(11)x2a2−(z−l)2b2=1,
where a and b are given by the fitting results of the hyperbola light beam.
The margin lines of the minimum angular resolution of human eyes (αe) are given by the following equation:
(12)x=±tan(αe2)(z−l−d).
Combining Eqs. (11) and (12), we can confirm the locations of the rear and front marginal depth planes. Therefore, the DOF of the RPII display can be defined as the distance between the two marginal depth planes:
(13)DOFWave=2−a4b2+a2b4tan(αe/2)2+a2b2d2tan(αe/2)2|a2−b2tan(αe/2)2|.
After obtaining the DOF calculation formula, we can use it to analyze the variations of DOF with different parameters. In the calculation process we assume that the number of correspondence pixels (H × V) always meets the requirement of (2w+1)≤min(M,N). Note that H × V is decided by the focal length f and the gap g according to Eqs. (3) and (4). It means that once f and g are given, H × V is fixed and can be calculated by the given f and g. The relationship between the viewing distance d and the DOFWave is given by Eq. (13). It shows that the DOFWave increases monotonously if d increases. Therefore, we will only discuss the variations of DOFWave with different focal length f, gap g, and MLA pitch p in this paper. Table 1 lists the parameters used in this section. The minimum angular resolution of human eyes is set to be αe = 1.662 × 10-2° [42], the mean wavelength is λ¯=5.5×10−4mm, and the viewing distance is d = 2500mm [45–47].
Table 1. Parameters used in DOF calculation
View Table | View all tables in this article
Table 3. Variation of DOFWave with different gap g
DOFWave have been calculated with different specifications according to Eq. (13). Tables 2–4 show the variations of DOFWave with different focal length f, gap g, and MLA pitch p, respectively.
Table 2. Variation of DOFWave with different focal length f
Table 4. Variation of DOFWave with different MLA pitch p
From the results shown above, we can see that the values of DOFWave highly depend on focal length f, gap g, and micro-lens pitch p. The variations of DOFWave are not monotonic as we change these parameters, and the optimal DOFWave values can be determined by multi-parameter optimization [48,49].
According to the above analyses, we designed and implemented an experiment to show the accuracy of the proposed method. To avoid light diffraction or aberration effects in the pickup process, we used Autodesk 3ds Max 2012 software to generate the elemental image array, and the obtained elemental image array was printed on a piece of high-quality photo paper with a Brother HL-4150CDN color printer to implement the optical display. The reconstructed 3D images were then captured by a Canon EOS 5D Mark II camera at a viewing distance of d = 2500mm. Table 5 shows the parameters used in the pickup and display experiments.
Table 5. Parameters used in the pickup and display experiments
To verify the proposed DOF calculation method, we compared the DOF calculation results with those calculated by geometrical optics and Gaussian beam methods as shown in Table 6..With given parameters, we calculated three groups of DOF values using three different DOF calculation methods. Here, DOFGeom, DOFGauss, and DOFWave refer to the DOF derived by geometrical optics method, Gaussian beam method, and wave optics method, respectively.
Table 6. DOF calculation results obtained from geometrical optics, Gaussian beam, and wave optics methods
We set up a 3D scene which consists of seven colorful "florets" located at seven different depth positions with Autodesk 3ds Max software 2012, as shown in Fig. 5.According to the DOF calculation results shown in Table 6 and the locations of the seven different "florets" given in Fig. 5, "florets" number 1 to 7 are within the range of DOFGauss, "florets" number 2 to 6 are within the range of DOFGeom, and "florets" number 3 to 5 are within the range of DOFWave.
Fig. 5 Schematic, not to scale, of the pickup process of RPII conducted in Autodesk 3ds Max 2012. Here, M × N = 110 × 110, f = 3.3mm, and p = 1.0mm.
The pickup process was conducted in a computer without the influence of diffraction or aberration effects, as shown in Fig. 5. The parameters used in the pickup process are listed in Table 5 and the generated elemental image array contains 110 × 110 elemental images, each with a resolution of 40 × 40 pixels, as given in Fig. 6(a).
Fig. 6 (a) Obtained elemental image array, and (b) experimental setup of the RPII display setup. Here, M × N = 110 × 110, H × V = 9 × 9, f = 3.3mm, p = 1.0mm, g = 3.7mm, and the resolution of each elemental image is 40 × 40 pixels.
In the optical 3D display process, as shown in Fig. 6(b), the elemental image array was printed on a piece of paper (as our display) and placed behind the MLA, which has identical parameters with the previous one used in the pickup process, with a separation of g = 3.7mm. Other parameters are given in Table 5. Figure 7 shows the captured display results.
Fig. 7 (a) Different perspectives of the reconstructed 3D image, (b) enlarged view of the center viewpoint, and (c) 2D image of the original 3D"florets" number 4 for reference.
From the experimental results, we can see that the reconstructed 3D "florets" number 1, 2, 6, and 7 which are located within the theoretically predicted range of DOFGauss or DOFGeom and out of the range of DOFWave appear blurry. However, "florets" number 3, 4, and 5 which are located within the theoretically predicted range of DOFWave and also within the ranges of both DOFGauss and DOFGeom appear clearer and smoother. What's more, by comparing Fig. 7(b) with Fig. 7(c), we can see that 3D "florets" number 3, 4, and 5 are reconstructed more correctly than the rest ones with less distortion.
The results demonstrate that the effect of multiple micro-lenses and diffraction strongly affect the DOF in an RPII display. Even though we have neglected the pixel size of the display, the proposed DOF calculation method based on wave optics is more accurate than both geometrical optics and Gaussian beam methods. Experimental results demonstrate the accuracy of the proposed method.
In this paper, we analyzed the DOF of the integral imaging display with multiple micro-lenses using wave optics. We first derived the light intensity distribution with multiple micro-lenses, and then the DOF was calculated by combining hyperbola fitting of the diffraction intensity patterns and the minimum angular resolution of human eyes. With given system parameters, we determined several groups of DOF values and analyzed the variations of them under different situations. Finally, optical experimental results confirmed the accuracy of the proposed method. In the future work, other parameters such as viewing resolution and viewing angle will be studied as well as the pixel size of the display panel. These analyses can be quite beneficial for researchers to better understand and develop desired integral imaging displays.
This work is supported by the "973" Program under Grant No. 2013CB328802, the NSFC under Grant Nos. 61225022 and 61036008, and the "863" Program under Grant Nos. 2012AA011901 and 2012AA03A301. M. Martinez-Corral acknowledges financial support from projects DPI2012-32994 and PROMETEO2009-077. This work is also supported in part by Samsung Electronics Inc. under the Samsung Advanced Institute of Technology (SAIT) Global Research Outreach (GRO) Program.
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Aloni, D.
Arai, J.
Barreiro, J. C.
Blanche, P. A.
Burckhardt, C. B.
Chang, Y. C.
Chen, C. W.
Cho, M.
Daneshpanah, M.
Davies, N.
Deng, H.
Dohi, T.
Flores, D.
Furuya, M.
Gong, X. X.
Gu, T.
Haino, Y.
Hata, N.
Hong, K.
Hong, S. H.
Hoshino, H.
Hsieh, P. Y.
Huang, X.
Huang, Y. P.
Igarashi, Y.
Isono, H.
Ives, H. E.
Iwahara, M.
Jang, J. S.
Javidi, B.
Jaynes, C.
Jen, T. H.
Ji, C. C.
Jung, J. H.
Kawakita, M.
Kim, J.
Kim, S. K.
Kim, Y. H.
Lee, B.
Lee, K. H.
Li, D. H.
Li, G.
Li, L.
Li, S.
Liao, H.
Lin, W.
Lippmann, G.
Luo, C. G.
Martinez-Corral, M.
Martínez-Corral, M.
Martinez-Cuenca, R.
Martínez-Cuenca, R.
Matoba, O.
McCormick, M.
Min, S. W.
Mishina, T.
Mitani, K.
Moon, I.
Murata, H.
Nakajima, S.
Nakamura, J.
Navarro, H.
Norwood, R. A.
Okano, F.
Okui, M.
Onural, L.
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Park, J. H.
Peyghambarian, N.
Rokutanda, S.
Saavedra, G.
Sakuma, I.
Sato, M.
Shin, D.
Son, J. Y.
Son, W. H.
St Hilaire, P.
Stern, A.
Su, Y. R.
Takahashi, T.
Takaki, Y.
Tanaka, K.
Tao, Y. H.
Tay, S.
Thomas, J.
Tunç, A. V.
Ueda, M.
Voorakaranam, R.
Wang, F. N.
Wang, P.
Wang, Q. H.
Wang, Y. Z.
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Yamamoto, M.
Yang, L.
Yang, R.
Yeom, S.
Yöntem, A. Ö.
Yoshimura, M.
Yuyama, I.
C. R. Acad. Sci. (1)
IEEE Trans. Inf. Technol. Biomed. (1)
IEEE Trans. Vis. Comput. Graph. (1)
J. Disp. Technol. (7)
J. Opt. Soc. Am. A (5)
J. Soc. Inf. Disp. (1)
Jpn. J. Appl. Phys. (2)
Opt. Eng. (1)
Proc. IEEE (5)
Proc. SID Symp. Dig. (1)
Fig. 3 Cross sections and meridian sections (y = 0) of the diffraction intensity patterns on different depth planes (a) z = 20.0mm and (b) z = 26.0mm. Here, f = 4.0mm, g = 5.0mm, p = 0.8mm, λ ¯ = 5 . 5 × 1 0 − 4 mm, and H × V = 5 × 5.
Table 1 Parameters used in DOF calculation
Table 3 Variation of DOFWave with different gap g
Table 2 Variation of DOFWave with different focal length f
Table 4 Variation of DOFWave with different MLA pitch p
Table 5 Parameters used in the pickup and display experiments
Table 6 DOF calculation results obtained from geometrical optics, Gaussian beam, and wave optics methods
(1) DO F Geom =2 l 2 g×p p d ,
(2) DO F Gauss = 2l 4tan ( α e /2 ) 2 d 2 p 2 g 2 +4 p d 2 tan ( α e /2 ) 2 l 4 − p 2 l 2 p d 2 | 4tan ( α e /2 ) 2 l 2 g−g p 2 | ,
(3) w=⌊ f 2| g−f | ⌋ ,
(4) H×V={ ( 2w+1 )×( 2w+1 ) ( 2w+1 )≤min( M,N ) M×( 2w+1 ) M≤( 2w+1 )≤N ( 2w+1 )×N N≤( 2w+1 )≤M M×N ( 2w+1 )≥max( M,N ),
(5) ( x mn D , y mn D )=( g f mp, g f np ),
(6) P 00 ( x 0 , y 0 )=rect( x 0 p , y 0 p )={ 1 - p 2 ≤ x 0 ≤ p 2 ,- p 2 ≤ y 0 ≤ p 2 0 otherwise .
(7) t mn ( x 0 , y 0 )= P 00 ( x 0 −mp, y 0 −np )exp{ −j k 2f [ ( x 0 −mp ) 2 + ( y 0 −np ) 2 ] }.
(8) I mn ( x,y;z )=| 1 λ ¯ 2 gz ∫ ∫ −∞ +∞ exp{ j k 2g [ ( x 0 − x mn D ) 2 + ( y 0 − y mn D ) 2 ] } × t mn ( x 0 , y 0 ) ×exp{ j k 2z [ ( x− x 0 ) 2 + ( y− y 0 ) 2 ] }d x 0 d y 0 | 2 ,
(9) I( x,y;z )= ∑ m=−w,n=−w m=w,n=w I mn ( x,y;z ) .
(10) ∫ -r(z) r(z) I( x,0;z ) dx=0.84 ∫ -∞ ∞ I( x,0;z ) dx.
(11) x 2 a 2 − ( z−l ) 2 b 2 =1,
(12) x=±tan( α e 2 )( z−l−d ).
(13) DO F Wave = 2 − a 4 b 2 + a 2 b 4 tan ( α e /2 ) 2 + a 2 b 2 d 2 tan ( α e /2 ) 2 | a 2 − b 2 tan ( α e /2 ) 2 | .
Parameters used in DOF calculation
λ ¯ —Mean wavelength
l—Conjugate distance defined by 1 / l = 1 / f − 1 / g [41]
p—Pitch of MLA
αe—Minimum angular resolution of human eyes
f—Focal length of the micro-lens
DOFWave—DOF derived by wave optics method
d—Viewing distance between the eye and the conjugate plane
g—Gap between the display and the MLA; M × N—The total number of micro-lenses
H × V—The number of correspondence pixels
Variation of DOFWave with different gap g
f = 4.0mm, p = 0.8mm, d = 2500mm, αe = 1.662 × 10-2°, λ ¯ = 5.5 × 10−4mm
H × V
DOFWave (mm) 8.8 8.6 10.6 8.6 23.1 20.7 19.0 17.7
Variation of DOFWave with different focal length f
g = 8.0mm, p = 0.8mm, d = 2500mm, αe = 1.662 × 10-2°, λ ¯ = 5.5 × 10−4mm
f (mm)
DOFWave (mm) 17.7 22.8 29.9 12.7 17.3 14.9 17.2 17.2
Variation of DOFWave with different MLA pitch p
f = 3.0mm, g = 4.0mm, d = 2500mm, αe = 1.662 × 10-2°, λ ¯ = 5.5 × 10−4mm
p (mm)
DOFWave (mm) 13.8 11.5 9.9 8.6 7.7 6.9 6.3 5.8
Parameters used in the pickup and display experiments
Total number of micro-lenses (M × N)
Focal length of the micro-lens (f)
Pitch of the MLA (p)
Resolution of each obtained elemental image
40 × 40 pixels
Resolution of the Brother HL-4150CDN color printer
Resolution of the Canon EOS 5D Mark II camera
4368 × 2912 pixels
Gap between the display and the MLA (g)
Pixel size of the display (pd)
Viewing distance between the eye and the conjugate plane (d) 2500mm
DOF calculation results obtained from geometrical optics, Gaussian beam, and wave optics methods
DOF calculation methods
Gaussian beam
f = 3.3mm, g = 3.7mm, l = 30.525mm, p = 1.0mm, d = 2500mm, αe = 1.662 × 10-2°, λ ¯ = 5.5 × 10−4mm, pd = 0.025mm, H × V = 9 × 9.
DOF (mm) DOFGeom = 12.6 DOFGauss = 42.4 DOFWave = 5.8


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"The doctor discovers, one by one, the secrets of the human body." Andreas Vesalius (1514-1564), the Belgian anatomist who founded modern anatomy. In Italy, Vesaluis revolutionized the study of anatomy, ending the teaching of Galen and practicing direct observation by dissection. His results were published in 1543 in the famous book De Humani Corporis Fabrica (On Structure of the Human Body). The first accurate work on human anatomy, it included many descriptions and fine woodcuts. After this early success, he became a court physician and all but gave up research.


On the one hand, Yellow is amazing. It's bright, vibrant, and just plain Yellow. It's the most yellow of colors. And I've wanted a yellow Corvette for a very long time.
On the other hand, Torch red is classic, red, and goes much better with the brown interior, which is not a deal breaker, but I've almost always been stuck with black interiors.


Super is one of the best savings vehicles available to us all yet sometimes it can seem a bit scary and complex. The government is often tinkering with things which leaves the average Australian lacking confidence.
Dolman Bateman Financial are experts in super. We pride ourselves on our ability to analyse peoples' super funds and tell them what they should be earning and what fees they shouldn't be paying. It's a big industry, and we make sure our clients are getting the most from it.
Let us help you get the right fund for you; industry, personal, SMSF.


From Scratch is a show about the entrepreneurial life.
We meet with leading pioneers from the business world, the social sector, and the arts. From Scratch personalizes the lives of entrepreneurs by providing listeners with a candid, first-hand view of the launching process. Guests speak openly about their sources of inspiration, setbacks, helpful allies, and breakthrough moments.
Featuring business, social and cultural leaders in all stages of the building process, From Scratch informs those who are either initiating their own entrepreneurial lives or simply feeling curious about those who make new ideas happen.
A show about the entrepreneurial life.


Celine Dion has some competition! Superfan Celine Tam lived up to her namesake when she gave a stunning performance of "My Heart Will Go On" during an America's Got Talent audition. The nine-year-old girl from Hong Kong, who has a younger sister named Dion, impressed the judges with her breathtaking rendition and explained that her parents are massive Celine Dion fans.
"This is my dream being on America's Got Talent," said the adorable singer. "So I'm guessing your parents love Celine Dion?" asked judge Mel B. "Yes, of course," she replied. Celine went on to say that her dad first discovered her singing talent when they were in the car together. She explained: "When I was in the car, my dad's driving and suddenly I just sang "My Heart Will Go On" and he was like, 'Wow'."
"A Celine Dion song," remarked Mel, to which fellow judge Simon Cowell joked: "We worked that out Mel, there's a Celine Dion connection." Simon went on to say it was obvious the young contestant loved singing Celine Dion songs and wanted to be the next Celine Dion. He then quipped: "What artist are you going to be singing?" "Celine Dion, duh!" the young girl replied.
The judges, audience and viewers at home were blown away as the budding singer poured her heart out and sang the Titanic ballad. Celine's parents watched from backstage, and her mum was sweetly seen wiping away tears as she watched her daughter sing. She received a standing ovation at the end of the performance, and even a big smile from hard-to-please Simon.
Celine's parents and sister watched from backstage.
It's not yet known whether Celine has made it to the next round, although her audition clip on YouTube has already gone viral, amassing nearly eight million views in less than three days. And it seems the performer is no stranger to talent competitions. She starred in Hunan Broadcasting's Let's Sing Kids in 2014, and has also performed on Hong Kong's TVB and at China CCTV's Spring Festival Gala. Celine also entered Britain's Got Talent in 2015, but did not get past initial auditions.


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Mitsubishi Heavy Industries (MHI) has delivered two replacement steam generators for the third unit of Southern California Edison's (SCE's) San Onofre Nuclear Generating Station (SONGS).
MHI said that the replacement steam generators delivered for SONGS 3 are among the world's largest, each measuring approximately 20 metres in length, seven metres in diameter and weighing some 580 tonnes. Each of them contains about 10,000 heat transfer tubes.
Steam generators are crucial components of plants based on pressurized water reactors (PWRs), transferring the thermal energy generated in the reactor vessel from the primary coolant circuit to a scondary steam circuit that drives the turbine generator.
MHI said it received the order from SCE in September 2004 after winning an international bidding competition. The steam generators were manufactured at the company's Kobe Shipyard & Machinery Works in Japan and will replace existing units at SONGS 3 during its next refuelling and maintenance outage, scheduled for the third quarter of this year.
There are two pressurised water reactors at the SONGS plant, the 1070 MWe unit 2 and 1100 MWe unit 3, which entered service in 1983 and 1984, respectively. Replacement of the original steam generators will enable the plant to continue operating up to 2022. In February 2009, MHI delivered two similar replacement steam generators for SONGS 2, which were installed later that year.
The delivery of the four steam generators to the SONGS plant brings the total number of such jobs by MHI for US customers to six. Since 1970, MHI has supplied steam generators to all of Japan's PWRs as well as to numerous PWRs in other countries, including replacement steam generators which the company notes help to extend plant operating life as well as boosting safety and efficiency. It is Japan's only steam generator manufacturer.
The company has received overseas orders for 31 units, mainly from North America and Europe. The total reaches 125 units if steam generators and replacement units for the Japanese market are included.


When the peloton steps out for the 2018 edition of the Lagos City Criterium, they will be starring yet again in one of Nigeria's fiercest cycle race which heralds the start of the cycling season and attracts participation from within and outside the country. This season, the eleven teams being supported by the Sustainable Cycling Foundation will grace the race in their new line of jerseys which have been carefully crafted to tell unique stories.
Inspired by the profound desire to showcase our agents of change; brands that have stood by us as we continue to give hope and access to opportunities to the underserved through cycling, SCF alongside its creative consultants have thoughtfully designed and tailored each jersey towards these brands.
The junior professional category shows the aspirations of budding cyclists like Team Aspire being recharged by 9mobile while Bright Future and Velocity youth teams ride under the banner of Cycology, pioneer riding club and a champion of the cycling cause.
Goal Cycling Club will be pulling stunts of strategy with Strategic Education as its sponsor while Team Elevate will be banking on the soundness of its gears as it steps out in Velocare color.
Premium real estate developer, Cocoon Homes is the prime sponsor of United Racing Club in the professional category.
Also in this category, the passion of Team CC12 is fueled by Eterna-Castrol with Lubrik and Craneburg Constructions providing sturdy support behind Cyclotron and Sharks Racing Club respectively.
The all-female Team Dolphin are all lithe in their Alitheia Investment colours. Access Bank has chosen to be a trailblazer and they will be sponsoring a very special Team… Stay tuned for more on this.
These jerseys will be formally launched at the Team Presentation and briefing of the opening edition of the Lagos City Crits later this year.
We look forward to more individuals and corporations getting involved in supporting the development of grassroots cycling in Africa in whatever ways they are able to.
We appreciate the wonderful support to the bright future cycling club Ibadan and cycling sports in Nigeria. More power to your elbow.