LED surgical lighting system with multiple free-form surfaces for highly sterile operating theater application Peng Liu, Yaqin Zhang, Zhenrong Zheng,* Haifeng Li, and Xu Liu State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, China *Corresponding author: [email protected] Received 13 February 2014; revised 14 April 2014; accepted 19 April 2014; posted 23 April 2014 (Doc. ID 206126); published 23 May 2014

Although the ventilation system is widely employed in the operating theater, a strictly sterile surgical environment still cannot be ensured because of laminar disturbance, which is mainly caused by the surgical lighting system. Abandoning traditional products, we propose an LED surgical lighting system, which can alleviate the laminar disturbance and provide an appropriate lighting condition for surgery. It contains a certain amount of LED lens units, which are embedded in the ceiling and arranged around the air supply smallpox. The LED lens unit integrated with an LED light source and a free-form lens is required to produce a uniform circular illumination with a large tolerance to the change of lighting distance. To achieve such a dedicated lens, two free-form refractive surfaces, which are converted into two ordinary differential equations by the design method presented in this paper, are used to deflect the rays. The results show that the LED surgical lighting system can provide an excellent illumination environment for surgery, and, apparently, the laminar disturbance also can be relieved. © 2014 Optical Society of America OCIS codes: (220.2945) Illumination design; (220.3630) Lenses; (220.4298) Nonimaging optics; (230.3670) Light-emitting diodes. http://dx.doi.org/10.1364/AO.53.003427

1. Introduction

In the past, the halogen lamp coupled with a certain optical system has been widely used as the source of surgical lamps for long periods [1–3]. However, many shortcomings, such as infrared and ultraviolet rays (which could threaten the health of the patient and the doctor), nontunable correlated color temperature (CCT), large volume, low efficiency, and short lifetime, suggest that the halogen lamp may not be the best solution for surgical lighting [4–6]. Development of the LED technique gives people a good chance to solve the current problems for the surgical lighting system [7]. For instance, Mayshack presents a

1559-128X/14/163427-11$15.00/0 © 2014 Optical Society of America

surgical lighting system that is integrated with an incandescent source and red LEDs to control the color-rendering index [8]. After that, Marka proposes a real sense of an LED surgical lighting system, which only employs LEDs as the light source and uses a lighting controller to separately control the light modules to generate appropriate illumination zones [9]. This system shows the elegance of LEDs in surgical lighting. After several years’ commercialization, it has been proved that the LED surgical lighting system can relieve patients from IR and UV radiation and can significantly improve doctors’ visual perception with the tunable light spectrum [10]. Although the LED surgical lighting system possesses many advantages compared with the traditional system, laminar disturbance, which is mainly caused by the structure of the surgical lighting 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS

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system, is still not resolved [11]. As we know, in order to ensure a strictly sterile surgical environment, a ventilation system is widely used in the operating theater to remove airborne contaminants. For the present LED surgical lighting system, however, the light sources are usually fixed on several large disks, which are connected together through control linkages. It has been proved that such a configuration can disturb the laminar airflow distribution of the operation area and thus have an impact on the cleanliness of the bacteria-free wound area [11–13]. For instance, in a study focusing on airflow patterns and the diffusion of contaminants in an operating theater, results drawn from both experimental and simulation methods showed that the obstacles in the occupancy zone, such as the surgical lighting system, had a significant influence on the distribution of the contaminants [14]. In this way, the caused laminar disturbance may increase the possibility of wound infection and even threaten a patient’s life. For example, a detailed survey carried out in 1996 showed that in France 10.5% of nosocomial infections are contracted in the operation room [15]. Therefore it is urgent to find a better solution for these issues. In this paper, we present an LED surgical lighting system to solve these issues. This system contains a certain amount of LED units, which can be separately controlled and are elaborately arranged to alleviate the laminar disturbance. The LED lens unit is composed of an LED light source and a dedicated free-form lens, which can produce a uniform circular illumination with a large tolerance to the change of lighting distance to meet the requirements of this LED surgical lighting system. To achieve such a dedicated design, this paper also proposes an approach to design the LED lens unit, which is integrated with multiple free-form surfaces. The characteristics of this dedicated free-form lens are explored and

analyzed, and an optical model of this LED surgical lighting system is also constructed. This paper is organized as follows: Section 2 introduces the configuration of this LED surgical lighting system and presents key issues in designing this system. Also in this section, the method for designing the dedicated free-form lens is detailed. In Section 3, the optical performance of the LED unit is explored and analyzed in more detail, and the LED surgical lighting system is constructed. The conclusion is given in Section 4. 2. LED Surgical Lighting System and Dedicated Free-Form Lens A. Introduction of the LED Surgical Lighting System

The configuration of a typical traditional operating theater is shown in Fig. 1. Usually, the surgical lamp is posed between the air inlet and the operation table while the air outlets are located at the bottom of two opposite walls. In order to explore the air disturbance effects brought by traditional surgical lamps, the software ANSYS, which is a professional program in computational fluid dynamics (CFD), is used to simulate the air distribution in the operating theater (the results are shown in Fig. 2). During the simulation process, the velocity of the air from the inlet is 0.45 m∕s, the temperature around the air inlet is 298 K, and the K − ε model is adopted. It is obvious that air backflow exists, and thus vortex flow takes place between the surgical lamp and the operation table. This will have an impact on the cleanliness of the surgery area. The proposed LED surgical lighting system is shown in Fig. 3. This system contains a certain amount of LED units, which are embedded in the ceiling and arranged around the air supply smallpox. The air distribution of the operating theater with

Fig. 1. Configuration of a typical traditional operating theater. 3428

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Fig. 2. Air distribution of the traditional operating theater for (a) one specific cross section and (b) another cross section.

Fig. 3. Configuration of the proposed surgical lighting system.

this surgical lighting system is also analyzed by ANSYS and provided in Fig. 4. Obviously, the new proposed surgical lighting system showed no impaction to the laminar air distribution and thus can contribute a more sterile environment for surgery.

For the ceiling-embedded surgical lighting system, the LED lens units are the same and can be separately controlled. The LED lens unit consists of a high-power white LED and a free-form lens and is able to revolve around two axes. During the surgery,

Fig. 4. Air distribution of the operating theater with the new proposed surgical lighting system for (a) one cross section and (b) another cross section. 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS

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all the LED units are controlled to illuminate the same wound area to improve the irradiance level and the shadowless ratio of the surgical lamp. It is required that the LED unit should produce a uniform circular pattern with the radius of about 20 cm on the operation table with the lighting distance from 2 to 2.8 m. Besides, the illumination area should keep uniform in a certain depth [10] to provide the doctors with the depth information of operating organs. In other words, the spread angle of the emergent beam reshaped by the LED unit should be very small, and the LED unit should have a large tolerance to the change of lighting distance. The emission of the LED should be collected as much as possible to improve the energy efficiency. Such a dedicated design, which is the key to achieving this LED surgical lighting system, is a real challenge. This paper focuses on the optical design of this LED surgical lighting system and will show how to achieve such a dedicated LED unit in the following subsections. B.

LED Lens Unit

As mentioned above, we need to produce a uniform circular pattern with the radius of about 20 cm and lighting distance of about 2 m and collect the emission of the LED light source as much as possible. Namely, the maximum angle formed between emergent ray of the LED lens unit and the optical axis should be very small (about 5.7°). Obviously, a large angle of deflection should be achieved. Besides, the illumination pattern produced by the LED unit should have a large tolerance to the change of lighting distance. Generally, free-form surfaces, which can simplify the optical system and realize complicated illumination, are preferred when dealing with uniform illumination issues [16,17]. Nowadays, the design method of single free-form surface lens is so developed that even some special irradiance pattern can be obtained [18]. Of course, there are still some basic challenges remaining for the single free-form surface lens. For instance, because of the limitation by the refractive index of lens material, the marginal rays of the LED cannot reach the predetermined position if the rays are only refracted once by a single optical surface. Thus the irradiance tailoring method is used in most single free-form design works to avoid this situation. For example, a free-form lens with total internal reflection (TIR) structure, which is based on the idea of irradiance tailoring and also preferred for improving energy efficiency, can easily obtain an irradiance pattern with high uniformity [19]. However, the uniformity would deteriorate rapidly if the light distance varies from the predetermined value because the direction of the rays of output beam is irrelevant. This indicates that these single free-form surface design methods do not leave much room for additional requirements. Therefore at least two optical surfaces should be adopted if the uniformity and direction of rays are needed to be both ensured. Generally, the simultaneous multiple surface (SMS) optical design method 3430

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[20] is popular in dealing with double free-form surfaces issue. For example, Feng et al. [21] generalized the SMS method in designing a beam-shaping system with two free-form surfaces. Although the results turned out satisfied, the distance between the two free-form surfaces is so large that two free-form lenses had to be employed in the system. Obviously, this phenomenon added much complexity to the optical system, and it happened due to the principle of the SMS method. When luminous property of the light source and target irradiance distribution are given together with the start point of each surface, the SMS method begins to find an appropriate point for one optical surface based on the previously determined point on the other optical surface, and, unfortunately, this is not always a convergent process. Thus the two free-form surfaces may locate with a long distance, and sometimes, on the contrary, they even intersect with each other. This suggests the SMS method may be not the best solution here. Therefore many trials have explored other ways to construct multiple surfaces. For example, Moiseev et al. proposed an optical element with two aspherical surfaces by solving a set of explicit first-order linear differential equations [22]. This two surfaces technique can realize uniform illuminated areas with angular sizes of 0°–160°, but the uniformity obtained by the lens seems not good enough and is not quantified unexpectedly. Abandoning the previous design methods, we use a free-form lens integrated with two free-form surfaces, as shown in Fig. 5. The first free-form surface is used to collect the large angle emission of the source and produce a uniform circular pattern on the target plane with the radius of R1 (R1 > R0). Here R0 is the radius of the target circular pattern. Then this uniform circular pattern produced by the first free-form surface will be compressed by the second free-form surface to produce a uniform circular

Fig. 5. Geometrical relationship between the free-form surfaces and rays.

Fig. 6. (a) Geometric relationship between the first surface profile and rays. (b) Mapping relationship employed in the design.

pattern on the target plane with the radius of R2 (R2  R0). 1. Design of First Free-Form Surface A Cartesian coordinate system is established with its z axis along the optical axis, and the light source is located at the original of the coordinate system, as shown in Fig. 6(a). According to the Snell’s law, the relationship between the unit vector I1 of the incident ray and the unit vector I2 of the emergent ray at point P can be expressed by n2 × I2 − n1 × I1  n22  n21 − 2 × n2 × n1 × I2 · I1 1∕2 × N1 ;

(1)

where n1 is the refractive index of the medium around the free-form lens unit, n2 is the refractive index of the free-form lens unit, and N 1 is the unit normal vector at point P. According to Eq. (1), we can obtain a partial differential equation, which is given by ρ1φ 

ρ1 D2 sin φ − D1 cos φ ; D1 sin φ  D2 cos φ

(2)

where 

Fig. 7. Design principle of the second free-form surface.

be defined. Considering the rotational symmetry of the free-form surface, we employ a mapping shown in Fig. 6(b) and establish an energy relationship between the light source and the target illumination:

p D1  n1 x1 − ρ1 sin φ − sin φ x1 − ρ1 sin φ2  z1 − ρ1 cos φ2 p ; D2  n1 z1 − ρ1 cos φ − cos φ x1 − ρ1 sin φ2  z1 − ρ1 cos φ2

φ; ρ1  are the spherical coordinates of point P, ρ1φ is the first-order derivative of ρ1 with the respect to φ, and x1 ; 0; z1  are the coordinates of point T 1 . To solve this partial equation, a mapping representing the relationship between the incident ray of the source O and its target point on the illumination plane should

Z 2π ×

φN

0

I φ × sin φdφ  E × π × r2 ;

(3)

where I φ is the intensity distribution of the light source, and E is the irradiance distribution on the target plane. Then the differential equation can be 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS

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partial differential equation by which the second free-form surface is governed: ρ2β 

Fig. 8. Selection principle of the optimization variables.

numerically solved by the fourth-order Runge–Kutta formulas. 2. Design of Second Free-Form Surface The second free-form surface aims to compress the circular pattern produced by the first free-form surface to achieve the target pattern. As shown in Fig. 7, the point Qβ; ρ2  is an arbitrary point on the profile of the second surface. According to the design of the first free-form surface, similarly we can also obtain a

ρ2 D4 sin β − D3 cos β ; D3 sin β  D4 cos β

where D3  Ox –nI2x , D4  Oz –nI 2z , O  Ox ; 0; Oz  is the unit vector of the emergent ray, ρ2β is the firstorder derivative of ρ2 with the respect to β, and x; 0; z are the coordinates of the target point T. Since the unit vector I2 of the emergent ray at point P is also the unit vector of the incident ray at point Q, the position of point Q, of course, is determined by the emission angle φ of the light source. Next we will show how to establish the relationship between φ and β. The points O, P, and Q define a triangle, as shown in Fig. 7. Let jPQj  t, and we can obtain jρ1 I1  tI2 j  ρ2 :

(5)

According to Eqs. (2) and (5), t can be calculated by t

−b 

q b2 − a2 ρ21 − ρ22  a

;

(6)

Fig. 9. Flow diagram of the design process.

Table 1.

Design Parameters of LED Lens Unit

Parameter n1 n2 N θr jSAj jSBj R0 R1 z0

Description

Value

Refractive index of the medium around the free-form lens unit Refractive index of lens material Number of optimization points on the first free-form surface Maximum emission angle of LED collected by the first surface Distance between source S and the vertex of the first surface (A) Distance between source S and the vertex of the second surface (B) Radius of the desired circular pattern on the target plane Radius of the circular pattern produced by the first surface Lighting distance

1.0 1.4935 7 70° 10 mm 40 mm 200 mm 1800 mm 2000 mm

Fig. 10. Model of the free-form lens. 3432

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(4)

Fig. 11. Irradiance distribution produced by (a) the first surface of the initial design, (b) the second surface of the initial design, and (c) the optimized LED lens unit.

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Fig. 12.

Irradiance curves at different lighting distance.

where a  nρ21φ  ρ21 , and b  ρ1 ρ21φ  q ρ1 n2 − 1ρ21φ  n2 ρ21 . Then we can obtain the position of point Q, which is defined by Q  P  tI2   I  P1 N 1x I  P1 N 1z ; 0; ρ1 I 1z  t 1z ;  ρ1 I 1x  t 1x n n (7) q q where P1   n2 − 1ρ21φ  n2 ρ21 − ρ1 ∕ ρ21φ  ρ21 . Further we can get the relationship between φ and β, which is given by  nρ1 I 1x  tI 1x  P1 N 1x  : β  a tan nρ1 I 1z  tI 1z  P1 N 1z  

(8)

According to Eqs. (4) and (8), we can finally obtain the first-order derivative of ρ2 with respect to φ, which is defined by ρ2φ

∂ρ ∂ρ ∂β  2 2× : ∂φ ∂β ∂φ

Fig. 13. 3434

(9)

To numerically solve this equation, we also use a kind of mapping, which is similar to the one shown in Fig. 6(b). Then the lens unit can be constructed by some discrete data points. Besides, this design method can be easily generalized to achieve a kind of design where the emergent beam reshaped by the lens is parallel to the optical axis (z axis in Fig. 7) with a prescribed intensity distribution. In this case, we just need to assume that O  0; 0; 1 and R1  R2  R0 . The design method presented above is proposed for the point light source. In a compact design, the influence of the size of LED on the illumination will be obvious and cannot be neglected. Besides, this influence will be more obvious in a kind of design where the angle of deflection is very large, such as the design of the LED lens unit in the surgical lighting system proposed in this paper. Thus we employ an optimization method here to further improve the optical performance of the LED lens unit. This optimization uses the downhill simplex method and employs an approach of equal arc-length to determine the optimization points [23], as shown in Fig. 8. The merit function is represented by the relative standard deviation (RSD) of irradiance, which is defined by v u 2 M  u1 X Ei t RSD  ¯ −1 ; M i1 E

where Ei is the irradiance of each sample data point, ¯ is the average irradiance of all the sample points, E and M is the number of the sample points. A small value of RSD represents a higher uniformity. With this optimization, usually we can get a desirable design. The design process of the LED lens unit is shown in Fig. 9 3. Design Examples and Analysis

In this section, we will use the method introduced in Section 2 to design the LED lens unit and then construct an optical model of the LED surgical lighting

(a) Model of the TIR lens. (b) Comparison between the LED lens unit and the TIR lens.

APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014

(10)

Fig. 14. Irradiance distribution produced by the LED surgical lighting system at (a) three extreme positions on the operation table (see Media 1) and (b) the corresponding shadowless performance. 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS

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system with this LED lens unit. The light source is a 1 mm × 1 mm LED Lambertian emitter, and other design parameters are given in Table 1. According to the design theory presented in Subsections 2.B.1 and 2.B.2, we obtain an initial design of the LED lens unit, which is shown by Fig. 10. Figure 11(a) shows the illumination pattern produced by the first surface with the emitter source. It is obvious that the result is quite good. However, the irradiance distribution produced by the lens model with both the first and second surface deviates significantly from the target, as shown in Fig. 11(b). Obviously, we need to employ the optimization technique introduced in Subsection 2.A.3 to further improve the design. Figures 11(a) and 11(b) also indicate that we only need to adjust the second profile to improve the optical performance. Seven optimization points are determined by the method of equal arc-length, and 150,000 rays are traced during each optimization iteration. When the RSD becomes saturated, two million rays are traced to reduce the statistical noise in the final simulation. The optimized illumination pattern is shown in Fig. 11(c). Obviously, quite good irradiance uniformity with RSD of 0.015 is achieved, and the optical efficiency of the free-form lens is 93%. During the optimization process, 287 iterations are performed in order to find the best solution; each iteration costs 1 min in average, thus the whole optimization process costs about 5 h. To further explore the characteristics of this kind of LED lens unit, we change the lighting distance from 1500 to 2500 mm, according to the configuration of the LED surgical lighting system shown in Fig. 3. The irradiance curves at each distance are depicted in Fig. 12. The results show clearly that the uniformity within the desired illumination area remains almost unchanged for the LED lens unit presented in this paper. As a comparison, we also design a TIR lens to realize the same uniform circular pattern with the same lighting distance of 2000 mm, and we also change the lighting distance from 1500 to 2500 mm. The change of the irradiance uniformity is shown in Fig. 13. For the TIR lens, the uniformity changes significantly when the lighting distance deviates the target. Obviously, the optical performance of the LED lens unit is superior to that of the TIR lens; thus we obtain a compact and dedicated design, which has large tolerance to the change of lighting distance. This characteristic is important for the LED surgical lighting system presented in this paper. Then an optical model of the LED surgical lighting system is constructed by arraying 24 LED lens units around the air supply smallpox. The illumination produced by the surgical lighting system at three extreme positions on the operation table is analyzed, as shown in Fig. 14(a) and (Media 1). The yellow dashed line represents the operation table zone. The RSD at these three positions are, sequentially, 0.028, 0.093, and 0.034. Obviously, high uniformity is achieved at these extreme positions. Meanwhile, 3436

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Fig. 15. Configuration of the shadowless test simulation system.

a circular obstacle is posed 10 cm right above the illumination area in the ray tracing simulation system, which is shown by Fig. 15, to analyze the shadowless performance of this lighting system, and the results are shown in Fig. 14(b). The blue line represents the normalized irradiance value of the irradiance pattern without the obstacle, while the red line is the result with the obstacle. Compared with the previous result, the uniformity of the irradiance pattern with obstacle deteriorates slightly, and the RSD of the three extreme positions are 0.198, 0.451, and 0.375, respectively. This results claim an acceptable shadowless performance of the lighting system. Besides the fact that each LED unit can provide a uniform irradiance distribution, multiple LED units with different location are the main reason for the shadowless performance. Above all, this kind of dedicated LED lens unit ensures an excellent optical performance for the surgical lighting system. Meanwhile, all the results verify the feasibility and elegance of this design method presented in this paper. 4. Conclusion

This paper introduces an LED surgical lighting system, which can ensure the lighting conditions for surgery and air distribution of the operation rooms. It contains a certain amount of LED lens units embedded in the ceiling and arranged around the air supply smallpox. The LED lens unit is composed of

an LED light source and a dedicated free-form lens, which is required to produce a uniform circular illumination with a large tolerance to the change of lighting distance. To achieve these goals, a refractive structure integrated with two free-form surfaces is employed for the lens unit, and an approach is presented to design these two surfaces. In this method, each surface is governed by an ordinary differential equation, and an optimization technique is employed to further improve the optical performance of the lens unit. The characteristics of this LED lens unit are explored, and comparisons between this LED lens unit and a TIR lens are made. An optical model of the LED surgical lighting system also is established, and its optical performance is also analyzed. In addition, air distributions of the operation room with traditional or the proposed surgical lighting systems are analyzed. All results show clearly that this kind of dedicated LED lens unit designed by the approach presented in this paper can ensure an excellent optical performance for the surgical lighting system, and a more sterile surgical environment can be achieved. It is a pleasure for authors to acknowledge the funding support from the National High Technology Research and Development Program of China (863 Program No. 2012AA10A503), the National Natural Science Foundation of China (No. 61177015), the Fundamental Research Funds for the Central Universities of China, and Philips Brain-bridge Project. References 1. A. M. Smith and H. H. Frazier, “Surgical light with conical reflector (P),” U.S. patent 5,913,599 (22 June, 1999). 2. M. Hünerbein, R. Kummerfeld, G. Schlör, and J. Schröter, “Operation room light fixture having two light sources and a control unit (P),” U.S. patent 7,401,944 B2 (22 July, 2008). 3. M. Scholz, “Operation theater lamp (P),” U.S. patent 5,178,452 (12 January, 1993). 4. D. L. Bourke, K. Yee, and L. Mark, “Severe burn caused by an operating room light,” Anesthesiology 79, 171–172 (1993). 5. W. C. Beck and R. F. Heimburger, “Illumination hazard in the operating room,” Arch. Surg. 107, 560–562 (1973). 6. U. Matern and S. Koneczny, “Safety, hazards, and ergonomics in the operating room,” Surg. Endosc. 21, 1965–1969 (2007). 7. K. Kobashi and T. Taguchi, “Warm white LEDs lighting over Ra = 95 and its applications,” Proc. SPIE 6486, 648610 (2007).

8. A. C. Mayshack, T. J. Brukilacchio, L. W. Noble, A. Pievsky, B. Boulant, P. B. Elterman, and B. J. DiCarlo, “Illumination system adapted for surgical lighting (P),” U.S. patent 6,513,962 B1 (4 February, 2003). 9. R. Marka, M. Vogl, and C. Bartenbach, “Multiple module lamp (P),” U.S. patent 7,513,645 B2 (7 April, 2009). 10. A. J. Knulst, L. P. Stassen, C. A. Grimbergen, and J. Dankelman, “Choosing surgical lighting in the LED era,” Surg. Innov. 16, 317–323 (2009). 11. M. L. Pereira and A. Tribess, “A review of air distribution patterns in surgery rooms under infection control focus,” Ther. Eng. 4, 113–121 (2005). 12. W. Lu and A. T. Howarth, “Modeling and measurement of airflow and aerosol particle distribution in a ventilated two-zone chamber,” Build. Environ. 31, 417–423 (1996). 13. M. Woloszyn and J. Virgone, “Diagonal air-distribution system for operating rooms: experiment and modeling,” Build. Environ. 39, 1171–1178 (2004). 14. F. Memarzadeh and A. Manning, “Reducing risks of surgery,” Ashrae J. 2, 28–33 (2003). 15. CTIN. Enquete Nationale de Prevalence des infections nosocomiales, Mai-Juin 1996 comite technique national des infections nasocomiales – secretariat d’Etat a la sante et a la securite sociale. Direction Generale de la Sante. Direction des Hopitaux (1997). 16. Y. Luo, Z. X. Feng, Y. J. Han, and H. T. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18, 9055–9063 (2010). 17. W. Tai and R. Schwarte, “Design of an aspherical lens to generate a homogenous irradiance for three-dimensional sensors with a light-emitting-diode source,” Appl. Opt. 39, 5801–5805 (2000). 18. R. Wu, L. Xu, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “Free-form illumination design: a nonlinear boundary problem for the elliptic Monge–Ampére equation,” Opt. Lett. 38, 229–231 (2013). 19. Z. Zheng, X. Hao, and X. Liu, “Free-form surface lens for LED uniform illumination,” Appl. Opt. 48, 6627–6634 (2009). 20. P. Benítez, J. C. Miñano, J. Blen, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1502 (2004). 21. Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double free-form optical surfaces,” Opt. Express 21, 14728–14735 (2013). 22. M. A. Moiseev, S. V. Kravchenko, L. L. Doskolovich, and N. L. Kazanskiy, “Design of LED optics with two aspherical surfaces and the highest efficiency,” Proc. SPIE 8550, 85502N (2012). 23. P. Liu, R. Wu, Z. Zheng, H. Li, and X. Liu, “Optimized design of LED free-form lens for uniform circular illumination,” J. Zhejiang Univ. Sci. C 13, 929–936 (2012).

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LED surgical lighting system with multiple free-form surfaces for highly sterile operating theater application.

Although the ventilation system is widely employed in the operating theater, a strictly sterile surgical environment still cannot be ensured because o...
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