This study employs a sub-module concept to develop high-brightness light-emitting diode (HB-LED) fishing light arrays to replace traditional fishing light attractors. The horizontal/vertical (H/V) plane light intensity distribution curve (LIDC) of a LED light source are mapped to assist in the design of a non-axisymmetric lens with a fish-attracting light pattern that illuminates sufficiently large areas and alternates between bright and dark. These LED fishing light attractors are capable of attracting schools of fish toward the perimeter of the luminous zone surrounding fishing boats. Three CT2 boats (10 to 20 ton capacity) were recruited to conduct a field test for 1 y on the sea off the southwestern coast of Taiwan. Field tests show that HB-LED fishing light array installed 5 m above the boat deck illuminated a sea surface of 5 × 12 m and achieved an illuminance of 2000 lx. The test results show that the HB-LED fishing light arrays increased the mean catch of the three boats by 5% to 27%. In addition, the experimental boats consumed 15% to 17% less fuel than their counterparts.
© 2012 OSA
In recent decades, environmental protection has become a frequently discussed topic. Considering the current context of low-carbon economy, the replacement of energy-inefficient traditional lamps with highly energy-efficient light-emitting diodes (LEDs) has become an inevitable trend. Although LEDs have been applied widely to replace ordinary light sources, they are rarely used in the fishing industry, which relies heavily on high power lamps such as incandescent lamps. Therefore, this study presents a proposal for substituting LED fishing light attractors for traditional, energy-inefficient types to reduce the fuel consumption of fish-attracting lamps on fishing boats. Traditional fishing lamps are primarily omnidirectional light sources. This implies that the majority of the light beams produced using large quantities of fuel are dispersed in the air, rather than being area-focused to attract schools of fish. Furthermore, only the light beams with a wavelength between 450 and 570 mm transmitted by traditional fishing lamps have sufficient power to penetrate water; other wavelengths are easily absorbed by seawater . Consequently, to improve the penetration power of an underwater light, the output of traditional fishing light attractors must be increased, resulting in energy wastage. Furthermore, excessive luminous intensity may cause fires or harm the fish larvae, thereby resulting in the depletion of fish resources.
Several studies have examined alternatives light sources for fishing light attractors. Okamoto et al. designed LED fishing light poles with fixed wavelengths to lure Pacific sauries by combining LED fishing light attractors with traditional fishing lamps . Their results showed that fuel consumption was reduced by 55% while maintaining similar catch volumes. In addition, Choi et al. employed blue-light LEDs in the design for a squid attractor . Their experimental results showed that the LED squid attractor performed as well as a metal halide lamp. Based on these findings, LED-based fishing light attractors are a feasible alternative to traditional lamps. However, recent studies on LED fishing light attractors have primarily focused on the fish’s response to particular wavelengths and ignored light pattern designs. Consequently, their luminous efficiency was unsatisfactory and the energy-efficiency advantages of LEDs were lost. In view of that, this study employs a method for mapping the horizontal/vertical (H/V) plane light intensity distribution curve (LIDC) to design a lens that produces a fish-attracting light pattern. Compared with LED fishing light attractors discussed in extant literature, the proposed LED fish-attracting light and lens enhances the overall optical efficiency and achieves the goal of energy conservation.
Some of the sea fish has positive phototaxis which is a kind of taxis, or locomotory movement, that occurs when a whole organism moves in response to the stimulus of light. Phototaxis is called positive if the movement is in the direction of increasing light intensity. The positive phototaxis of fish can be divided into the following two stages: (1) fish swim toward a light source after being stimulated by the light ; and (2) fish linger below the light source. However, the fish attracted to the light swim away from the light source after a time passes because of desensitization fatigue, or environmental change . Therefore, we propose the design of a fish-attracting light pattern that alternates between bright and dark. The proposed design successfully attracted schools of fish that lingered for a long time at the edge of the perimeter of the luminous zone. To achieve a uniform light pattern, LED array light sources are frequently designed in compliance with Sparrow’s criterion to obtain the maximum flatness when two functions are added together . To achieve the most uniform distribution of illuminance intensity, Moreno et al. employed the Sparrow’s criterion to determine the distance between LED modules and the optimal arrangement of an LED array [6,7]. Similarly, with the help of Sparrow’s criterion, Wang et al. presented a novel reverse method for the design of freeform lens and observed the LIDC required by a single LED . Subsequently, the obtained LIDC was employed to design the lens for a LED to realize the most uniform illuminance of a LED array [9, 10]. This lens design process is conducted in accordance with prescribed illuminance of the target plane; therefore, it is called luminous energy mapping [11, 12].
In addition, other design methods exist, such as the trial-and-error and tailored methods . However, these methods require complex calculation and repetitive tests, so they are difficult, time-consuming, and energy-inefficient. Based on this discussion, we have followed the LIDC mapping method to design a non-axisymmetric lens. The lens produces a fish-attracting light pattern that illuminates a sufficient area and produces alternating light and dark zones. The method for mapping luminous energy was adopted by extant literature because the primary concern was the illuminance intensity distribution of the target plane. In contrast, the method for mapping the LIDC in this study maps the horizontal and vertical planes separately. This allows the specifications for the required lens to be determined rapidly and directly. During the design phase of this study, LED array fishing lights were divided into the following three categories (in descending order of size): LED arrays, modules, and sub-modules. First, according to Sparrow’s criterion, the LIDC required by the sub-modules was determined and LIDC mapping was conducted to design the outer form of the sub-module lens. A specific number of sub-modules were then assembled into a single LED module. Finally, the developed LED fishing light attractors were arrayed on a fishing boat and an effective fish-attracting light pattern with high illuminance that alternates between bright and dark was produced. Traditional or LED fishing light attractors that have been discussed in extant literature only provided uniform illuminance. To eliminate that shortcoming, this study has developed a LED array fish-attractor that efficiently lures schools of fish to the perimeter of the luminous zone around the fishing boats.
Finally, problems with traditional fishing lights that employ incandescent lamps include inefficient energy consumption, inefficient lamp performance, short life time, and excessive generation of heat and ultraviolet light. Therefore, we present the design and development of a highly efficient fishing light that uses a LED array fish-attractor. The proposed device will strengthen fishery management through energy conversation, thereby reducing the environmental impact of fishing activities.
2. Design method
When fishing light attractors are designed, the primary concerns include area of illumination, illuminance intensity, and a light pattern that alternates between bright and dark. Specifically, illuminated areas and luminous intensity define the functional range, whereas the alternating distribution of brightness and darkness can extend the time that schools of fish remain in proximity to the targeted area. Therefore, we employ a LED array in the design of an underwater polarized light, specifically, a fish-attracting light pattern, as shown in Fig. 1 .
The discussed fish-attracting light pattern attracts schools of fish to the perimeter of the luminous zone around the boats. The light pattern is based on the positive phototaxis of fish and on the alternating distribution of brightness and darkness. During the design process, Sparrow’s criterion was employed to calculate the LIDC of the LED sub-module and the LIDC mapping method was adopted to develop the device lenses. A group of sub-modules were then assembled into a single LED lighting module. Finally, according to the requirements of the illuminated areas, the proposed LED array light was constructed, thereby obtaining a fish-attracting light pattern that alternates between bright and dark. Figure 2 shows the schematic diagram of the proposed LED array. With a chip-on-board LED as the light source, the sub-module depends on the lenses to change its LIDC, thereby satisfying the required fish-attracting light pattern of a single LED module. The following section details the design of the lens that is responsible for the fish-attracting light pattern.
2.1 LIDC analysis of sub-module lens
Figure 3 shows the schematic diagram of the sub-module lens array and the target plane. In the diagram, d represents the interval between two sub-module lenses, z0 represents the distance between the light source and the target plane, N represents the total number of sub-modules, and E0 to E4 are randomly-selected reference points that define the illuminated area. In accordance with relevant literature , the formula for the LIDC of the sub-module on the vertical plane I(Φ) can be expressed as the Tayler series expansion of cos(Φ):
where a0 to a4 represent the coefficients of the exponential terms and Φ represents the emitted angle of LED. In addition, the illuminance intensity at any point of the illuminated area on the target plane is expressed as:
To make I(Φ) distribute uniformly on the target plane, Sparrow’s criterion is employed to calculate a0 to a4 of I(Φ). It is a criterion for the resolution of two light sources, according to which the light sources are resolved if the maximum light intensity of their combined diffraction pattern is equal to the light source. Sparrow’s criterion involves the conditions that satisfy the maximum flatness ; therefore, it can be employed to adjust d, thereby achieving the optimal uniformity, as expressed in the following formula:
Thus, it is established that the derivative of the slope that satisfies E(x, y, z0) at the origin (x = 0, y = 0) is 0, implying that the illuminance near the origin is uniform. Furthermore, to describe the uniform illuminance on the whole target plane, the reference points E1 to E4 in Fig. 3 require consideration. When the level of uniformity is limited to 80% to 120%, the following formula is obtained:
Through Eq. (3) and Eq. (4), the formula for the LIDC of the sub-module on the vertical plane was obtained, namely, I(Φ), similarly to that defined in Eq. (1). However, because the fish-attracting light pattern alternates between bright and dark, the sub-module lens could not be designed based on axial symmetry. If axial symmetry had been followed, a single LED module would have produced a circular light pattern. Thus, several light patterns would have overlapped if numerous LED modules had been arrayed and a light pattern that alternated between bright and dark would not have been realized efficiently unless the interval between the LED modules had been lengthened. Because there is not much space on a fishing boat, it is not desirable to increase the interval between LED modules. Therefore, we have designed a non-axisymmetric sub-module lens instead. Specifically, owing to rectangular illuminance distribution, the new LED fishing light attractor produced a light pattern with alternate brightness and darkness. However, a LED light source typically produces an axisymmetric light pattern that with a Lambertian distribution LIDC on the vertical plane. For this reason, we employed the LIDC mapping method for vertical and horizontal planes to rapidly determine a non-axisymmetric light pattern. Thus, the fish-attracting light pattern was designed successfully.
2.2 The method for LIDC mapping
The practical design commenced with the LED light source, the luminous intensity and light emission angle which is correlated with a cosine function. However, the correlation depends on its encapsulant and semiconductor region shapes. Therefore, the luminous intensity distribution of the LED can be defined as :
In Eq. (6), Φ1/2 is the light-emitting view-angle of the LED, defined as the angle of which the luminous intensity is half of ILED(0). To simplify the calculation process, m = 1 was substituted into Eq. (6); that is, the LED light source was regarded as a perfect Lambertian emitter, with Φ1/2 at approximately 60°. The consequent LIDC of LED on the vertical and horizontal planes are shown in Figs. 4(a) and 4(b), respectively. Unlike extant literature [8–12] that adopted the light pattern on a target plane as the design requirements, this study focuses on the lens LIDC requirements. Thus, the problems are reduced to only those concerning corresponding angles. Based on the corresponding angles, the points on the lens and their corresponding reversed normal vectors are calculated; eventually, the lens is developed. Therefore, during the design process, the most crucial concept is determining a LIDC that is compatible with the lens. Figure 5 shows the ideal LIDCs of the rectangular light pattern for this study. Figure 5(a) shows the LIDC on the vertical plane and Fig. 5(b) shows that on the horizontal plane. The LIDC on the horizontal plane is used to adjust the luminous intensity after the light beams traveled through the lens. Furthermore, the length-to-width ratio of the light pattern is regulated by the ratio of a and b in Fig. 5(b).
After the LIDCs on the vertical and horizontal planes were obtained, the angle-mapping relationships between the light source and the light pattern in two directions could then be determined. The law of conservation of energy is employed to determine the corresponding angles. Ideally, after a light source travels through a lens, its total energy remains unchanged. We divided the LIDC of LED into x parts and each has same luminous flux. Then each corresponding angle can be calculated by integrating the LIDC which needed by sub-module lens. Therefore, the LIDC relationship between the light source and the light beams traveling through the lens can be expressed vertically and horizontally in the first quadrant. Next, the mapping relationship between the light emitted angle of LED and lens on vertical plane ILED(Φ) and ILens (Φ), as well as that between the light emitted angle of LED and lens on horizontal plane ILED(θ) and ILens(θ), are determined. The relationship between various corresponding angles of the light source and the light beams traveling through the lens is identified. Finally, Snell’s law is employed to identify the points on the lens and their corresponding normal vectors. In accordance with the vector formula, Snell’s law is expressed as:Eq. (7).
Based on , the main curve of a lens can be constructed, as shown in Fig. 6(a) . First, lens height value L is set with θ = 0 and Φ = 0. Thus, starting point P11 is obtained and tangent plane T11 that passes through P11 and is vertical to the first incidence vector (I11) is identified. Next, the intersection of the tangent plane (T11) and the second incidence vector (I12) is located by the second point (P12) of the main curve. Similarly, all remaining points on the main curve (P13 to P1N) are identified. Thus, the main curve of the lens is constructed. After the main curve is obtained, the remaining minor curves are calculated using a similar method, as shown in Fig. 6(b). First, point P12 on the main curve is taken as the starting point, and then P22, and P32…PM2 are identified similarly. By repeating the procedure, P13 to P1N are taken as the main points of the other minor curves, thereby identifying points P23 to PM3, P24 to PM4…P2N to PMN. Finally, a complete lens was developed.
2.3 Analysis and design of the lens producing a fish-attracting light pattern
Six LED lighting modules were arrayed on each side of the boat to produce a fish-attracting light pattern on both sides. That is, each boat was equipped with twelve LED lighting modules, thereby forming a LED array fish-attractor. Based on the desired fish-attracting light pattern, the authors set 1:2.5 as the ratio of a and b in the LIDC on the horizontal plane. Furthermore, the size of a single LED module is 550 mm × 365 mm. According to relevant literature , the LED module is regarded as a far field light source by considering the size of single LED module and the illuminated area. Therefore, it is only necessary to design the sub-module in a single LED module and then array the LED modules to produce the fish-attracting light pattern. Thus, from the LIDC on the vertical plane of the sub-module, a specific angle (θi) is selected, which had an LIDC on the vertical plane, namely, Iθi(Φ). Then, any LIDC corresponding to angle θ (i.e., Iθ(Φ)) could be inferred through its LIDC on the horizontal plane. As stated, the ratio of a and b is 1:2.5; therefore, the light pattern produced by a single LED module requires 5 m in the y direction and 2 m in the x direction on the sea surface. Based on the forgoing relationship, the LIDC (θ = 0) on the vertical plane of the sub-module (I0(Φ)) can be obtained from Eq. (1). Furthermore, distance d between the light source and the illuminated area on the sea is 5 m, with an illuminated area of 2 × 5 m. Meanwhile, four reference points (E1 to E4) in the illuminated area are randomly selected, and Eq. (3) is used to calculate the coefficients Eq. (1): namely, a0 = 0.8485, a1 = 2.7637, a2 = −14.533, a3 = 17.6669, and a4 = −6.6957. Consequently, when the 3-D fish-attracting lens was constructed, I0(Φ) could be adopted as a benchmark. The outer appearance of the sub-module lens was then drawn based on I0(Φ) and the LIDC on the horizontal plane. Equation (7) was then used to identify several lens curves, as shown in Fig. 7(a) . Finally, a lofting method  is employed to determine the outer curved plane of the sub-module lens, as shown in Fig. 7(b).
3. Results and discussions
3.1 Results of simulation
The sub-module lens data were entered into an optical and illumination design software package (TracePro) for simulation testing. In compliance with the design requirements, a chip-on-board LED (LUSTRON X5) is used as a light source (1050 lm, Φ20 mm). The distance between the target plane and the light source is 5 m; furthermore, the lens material is polymethyl methacrylate, with an index of 1.4935. Figure 8(a) shows the model of the lenses within a single LED module, which contain ten sub-module lenses. As shown in Fig. 8(b), the light beams emitted from the LED light source are refracted by the lenses and form a rectangular illuminance intensity distribution on the observation plane 5 m from the light source. The illuminated area is approximately 5.5 × 2 m, and is slightly greater than the design requirements. Figure 8(c) shows the LIDC on the vertical plane after the LED light beams are refracted by the lens, whereas Fig. 8(d) shows the LIDC on the horizontal plane. Furthermore, Fig. 8(c) shows that the LIDC on the vertical plane is shaped like a bat’s wing; consequently, light beams on the observation plane are distributed uniformly, as shown in Fig. 8(b). In addition, the rectangular LIDC on the horizontal plane made the light beams spread rectangularly on the observed plane. To validate the performance of the LED fishing light attractor on the sea surface, six LED modules were arrayed at an interval of 2 m during the simulation test. Figure 8(e) shows the analysis diagram of the illuminance intensity calculated by the lighting simulation software DIALux. The lighting modules in the simulation test were arrayed on the boat side and tilted at an angle of 45°, identical to how they would be arrange on a boat. Figure 8 shows that a fish-attracting light pattern was successfully created. With the water surface used as the observation plane, Fig. 8(f) shows that the mean illuminance is approximately 2100 lx when the LED modules were tilted. As shown in the discussed figures, the method for designing the fish-attracting light pattern employs sub-module lenses that change the original axisymmetric light pattern into a rectangular distribution of illuminance intensity. With such a rectangular light pattern, the minimum number of LED modules within the limited space on the fishing boat produces a light pattern that alternates between bright and dark.
3.2 Production and measurement of the LED array fish-attracting light
Figure 9(a) shows a physical sub-module lens and Fig. 9(b) shows its light pattern 5 m from the light source. Its illuminated area is 5 × 2 m, its maximum illuminance is 2100 lx, and its mean illuminance is 2000 lx. In this study, a goniophotometer system (Fig. 9(c)) is used to measure the sub-module lens, with the measured results shown in Fig. 9(d). The horizontal LIDC produced by the sub-module lens displayed a rectangular distribution that satisfied the design requirements. In accordance with the simulation result in this study, ten sub-modules were assembled into a single LED lighting module. Because each sub-module provides a luminous flux of 1050 lm, the total luminous flux of a single LED lighting module is 10 500 lm, with a power consumption of 200 W. Finally, to meet the requirements of a fishing boat, six LED lighting modules were used to form an LED array. Figure 10(a) shows the LED lighting modules arrayed on an actual fishing boat. The dimensions of the high-brightness LED lighting module are 550 × 365 × 125 mm, with a weight between 16 and 20 kg. Based on the simulation results of the LED fish-attracting light, six LED lighting modules were arrayed on each side of the top platform of a fishing boat, with a distance between two lighting modules of 2 m, and a total illuminated area of 12 × 5 m on the sea surface as shown in Fig. 10(b). The luminous intensity of each LED lighting module was 10500 lm, and its power consumption was 200W. After being field-tested, the LED array fishing light produced an illuminance of 1800 to 2100 lux in bright area and 450 to 490 lux in dark area on the sea surface. Figure 10(c) shows the actual distribution of illuminance intensity of the LED fishing light attractor measured near the pier. It was observed that in the horizontal direction, there was a 1.5 to 2 m-wide area of uniform illuminance with a separation of 0.5 to 1 m. Thus, there were six areas of uniform illuminance within 12 m measured, whereas a 5 m-wide area of uniform illuminance was measured in the vertical direction. The level of uniformity in the measured area was 80%, displaying alternate brightness and darkness of a fish-attracting light pattern. The following section details the use of the proposed LED array fish-attracting light in a fish-catching test at sea.
3.3 Comparison of mean catch and fuel consumption
To validate the practicality and energy-efficiency of the LED array fishing light, three CT2 fishing boats (Ship A, Ship B, and Ship C) were selected to undergo a one-year test off the southwestern coast of Taiwan. Ships A, B, and C were equipped with LED array fishing lights by 4kW metal halide lamps on August 23, July 30, and July 1, 2009 respectively. Afterwards, the authors boarded the boats several times and recorded the fishing process, as detailed below. As soon as the boat reached the destination, the fish finder and the fishing light attractors were activated. The fish finder was used to detect whether schools of fish had been attracted by the light source.
To understand the difference between traditional and LED fishing light attractors, starting from January, 2010, we recorded the catch volume and fuel consumption of the three boats (Fig. 11 ). Figure 11(a) shows that Ships A, B, and C had a mean catch volume per trip of 1866, 2711, and 1945 kg, respectively, before they were equipped with developed LED fishing light attractors. After being equipped with LED fishing light attractors, Ships A, B, and C had a mean catch per trip of 2257, 2866, and 2487 kg respectively. In other words, the three boats increased their mean catch by 20%, 5%, and 27%, respectively. This evidence validates the effectiveness of the proposed fish-attracting light pattern for attracting fish. Regarding fuel consumption, this study obtained information on fuel refilling and working hours of the three boats (Fig. 11(b)). Prior to the installation of the developed LED array fishing lights, Ships A, B, and C had a mean fuel consumption of 46, 77, and 52 L/h, respectively. After the LED array fishing lights were installed, the three boats had a mean fuel consumption of 39, 65, and 43 L/h, respectively, thereby reducing their fuel consumption by 15.2%, 15.6%, and 17.3%, respectively. These results show that replacing traditional high-pressure sodium lights with LED lights reduces fuel consumption efficiently. In addition, with a properly-designed light pattern, LED lights perform well at attracting fish. The field test indicates that LED array lights are highly applicable to lighting-based fishery.
In this study, LED fishing light attractors were employed as a light source to replace traditional ones. The method for LIDC mapping on horizontal and vertical planes was employed to design sub-module lenses that produced a fish-attracting light pattern with an alternating distribution of brightness and darkness; thus, the optical design of fish light attractors were succeed. Regarding illuminance in the bright and dark areas, the LED fishing light attractor produced a mean illuminance of 2000 lx and 470 lx, respectively. The overall illuminated area was 12 × 5 m. To verify the fish-attracting efficiency of the proposed LED array fish-attracting lights developed by the authors, three CT2 fishing boats were selected to perform a test for 1 y at sea off the southwestern coast of Taiwan to determine their mean catch volume and fuel consumption. The test results show that the proposed LED array lights reduced fuel consumption by 15% to 17%. In addition, the mean catch of one boat performed as well as when it was equipped with traditional fishing lamps. The two others increased their mean catch by more than 20%, meaning a considerably better fish-attracting effect. In conclusion, the LED fishing light attractors out-performed traditional lights for fuel consumption and fish-attracting efficiency. To substitute the LED system for the traditional system will provide a novel concept of energy conservation for traditional, energy-consuming, and lighting-based fishery.
The authors would like to thank National Science Council (NSC) for their financial supports to the project (granted number: NSC 100-2628-E-006-019-MY3, and NSC 98- 2221-E-006-260-MY3) and College of Engineering, National Cheng Kung University financial supports (5Y5M).
References and links
1. T. Okamoto, K. Takahashi, H. Ohsawa, K.- Fukuchi, K. Hosogane, S. Kobayashi, M. Moniwa, K. Sasa, H. Yoshino, H. Ishikawa, M. Harada, K. Asakura, and H. Ishii, “Application of LEDs to fishing lights for Pacific saury,” J. Light Vis. Environ. 32(2), 88–92 (2008). [CrossRef]
2. J. S. Choi, S. K. Choi, S. J. Kim, G. S. Kil, and C. Y. Choi, “Photoreaction analysis of squids for the development of a LED-fishing lamp, ” in Proceedings of the 2nd International Conference on Maritime and Naval Science and Engineering, (Brasov, Romania, 2009), pp.92–95.
3. H. Fujiyasu, T. Ishigaki, K. Fujiyasu, S. Ujihara, N. Watanabe, S. Sunayama, and S. Ikoma, “LED and semiconductor photo-effects on living things,” J. Light Vis. Environ. 32(2), 222–225 (2008). [CrossRef]
4. M. Marchesan, M. Spoto, L. Verginella, and E. A. Ferrero, “Behavioural effects of artificial light on fish species of commercial interest,” Fish. Res. 73(1-2), 171–185 (2005). [CrossRef]
5. G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook (SPIE Press, 1989).
6. I. Moreno, “Configurations of LED arrays for uniform illumination,” Proc. SPIE 5622, 713–718 (2004). [CrossRef]
9. K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009). [CrossRef]
10. K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific Light-Emitting Diode packaging,” Opt. Express 18(2), 413–425 (2010). [CrossRef]
14. D. Wood, Optoelectronic Semiconductor Devices (Prentice-Hall International, 1994).
15. I. Moreno and C. C. Sun, “LEDs array: where does far-field begin,” Proc. SPIE 7058, 70580R, 70580R-9 (2008). [CrossRef]
16. L. Piegl and W. Tiller, The NURBS Book 2nd ed (Springer, 1996).