Low-Cost Continuous-Wave-Laser (CW Laser) Digital Particle Image Velocimetry

Abstract

The invention of a Low-Cost alternating color-pulse digital particle-image velocimetry DPIV (Digital Particle Image Velocimetry) system is proposed. In the proposed system Low-Cost basic equipments are used such as a continuous-wave laser in mixed mode, a CCD (Charge Couple Device) camera, a PMT (Photo-Multiplier Tube), an image-processing card, a PC (personal computer) etc., with an add-on alternating-color planar laser-sheet generating facility to achieve the purpose of DPIV (Digital Particle Image Velocimetry) of planar velocity measurements. With the add-on facility, the laser beam from the continuous-wave laser operated in mixed mode is turned into a planar laser sheet with alternating color at a designated frequency. The CCD (Charge Couple Device) camera captures the alternating-color images of the flowfield seeded with small particles. The images are then sent to a personal computer for analysis of the magnitude and direction of the velocity distribution of the flowfield.

Description

FIELD OF THE INVENTION

[0001] This invention disclose a Low-Cost Continuous Laser DPIV (Digital Particle Image Velocimetry). The photograph of a particle flow field, taken by the CCD (Charge Couple Device) and processed by a PC (personal computer), can be used to detect a particle's direction and velocity, its moving locus in the flow field, and accordingly to determine the particle's 2-D velocity and the velocity's spatial distribution.

BACKGROUND OF THE INVENTION

[0002] In early fluid mechanics, such an interferable measurer as Hot Wire Anemometer or Pitot Tube was put in a flow field to take data at a certain point, and Flow Visualization Techniques to observe the qualitative data like geometric distributions of streamlines, shapes of flow fields, etc., and thus to learn the properties of flow fields.

[0003] With the brand-new and flourishing development in Optics, Electronics, image processing, Laser technology, and digital computers, LDV (Laser Doppler Velocimetry) has been widely applied in measuring the single-point velocity in a flow field. Such “non-intrusive measurement” will both keep the integrity of a flow field and meanwhile improve the accuracy of the flow field velocity and Turbulence data. However, Single-point Measurement Technique can only obtain data at only one single point without immediate and complete velocity distribution information of an entire plane. Thanks to the efforts of forerunners, in late 70's, PSV (Particle Streak Velocimetry) was first reported by Simpkins, P. G et al. (J. of Fluid Mech. Vol.89, pp.665-671, 1978). A transitory Mie scattering photo of a flow field implanted with micro particles was taken by a CCD (Charge Couple Device), via scanning of laser or other resources of illumination, to analyze (either with the film or the picture) the moving loci of particles in the flow field, and accordingly to make clear the relation between the velocity of particles in a 2-D plane and their velocity distributions in a 3-D space. Equipment for such a velocity measuring method via loci was simple to manipulate, and velocity of particles could be easily figured out through manual analyses. But to complicated images of more and speedy particles, it failed to process and thus determine the exact velocity direction of a flow field.

DESCRIPTION OF THE PRIOR ART

[0004] Once the encoded flashes of different time lapses were used to determine the velocity directions: a single particle might leave line segments of different lengths in the image, and the velocity directions could thus be determined by comparing the segment length and its corresponding code. Similarly, this method was still of little use in processing complicated flow-field images. Late in 80's, two methods were applied: Young's Fringe Method reported by Meynart, R.(Applied Optics. Vol.19, □9, pp.1385-1386, 1983) and Auto-correlation Method by He, Z. H. et al. (Experimental Mechanics, pp.117-121, 1984). Since the operations of the former method were too sophisticated, a 2-D self-relation analysis was usually adopted instead. Nonetheless, these two methods still had trouble in determining the moving directions of particles, although they were helpful in rather complex images.

[0005] A digital particle image velocity measurement was thus invented to solve the abovesaid troubles. Equipment used in this DPIV (Digital Particle Image Velocimetry) method included Pulse Laser, CCD (Charge Couple Device) Camera, Fram Grab, PC (personal computer), and so on. A film of a flow field scanned by high-energy laser was taken by a CCD (Charge Couple Device), and then processed by using a Frame Grabber in a personal computer to capture images. For determination of velocity, a Single Image Self-relation Analysis was adopted; for velocity directions, two methods were available: either by exactly controlling the relative time of the Double Pulse laser flashes vs. actuations of the camera to determine the sequence of two images and then processing these two images with cross-correlation analysis method, or by using two lasers, with one of which delayed and passing Raman Tube to change its color, to take two images of different colors, and then using the cross-correlation analysis method to determine the velocity and its direction. It was sure that better measurements could be obtained by such method, but the outstanding high costs of the Double Pulse high-energy laser, Raman Tube for changing colors, complex delay controller, and high-speed Frame Grabber were not affordable for average research institutes and individuals.

[0006] Recently, due to the rapid development of digital color image techniques, different colors of an image could be easily separated. (The processing of the color separated images by cross-correlation analysis method is shown as FIG. 1.) The so-called digital color image camera, like common single-eye types, had a shotter time setting. When the shotter was activated, a green beam laser illuminated the particles of a flow field, making the particles scattering green beam-marked as the first time point; then a blue beam laser took turns and thus the second time point marked. As illuminated by the alternative green and blue beams, the same particle appeared in different colors at different positions while moving. The entire period from the beginning of green beam illumination to the end of blue beam illumination was completed during a shooting. In such a way, a digital color photo (101) was obtained, in which black solid marks stood for green beam images (102) and hollow ones for blue. Green and blue images could be separated since this kind of digital color photos (101) were comprised of three primary colors, i.e. red, blue and green, and thus could usually be separated by a personal computer installed with related programs. The purpose of the above-said image color separation (104) was to determine by the mathematic cross-correlation analysis (105) whether two points were left by the same particle respectively at different time and positions in the green and blue images. When the distance between the two points was figured out, then divided it by the time necessary for alternation from green to blue beams, and you could easily got the moving speed of the particle, said Particle Moving Speed (106). And just by comparing different color signals in the same image, the velocity direction of the flow field could be known, too. The Color alternating Image Velocity Measurement reported by Jaw, S.-Y. et al. (The 22nd Symposium on Naval Hydrodynamics, Washington D.C., U.S.A., 1998) was developed from the above method, in which a combined beam, produced by Argon ion laser, could be transformed into plane beams of two alternating colors by alternatively changing the laser wavelength via AOM (Acousto-Opto Modulator). Therefore, the images, taken by a CCD (Charge Couple Device) while a flow field was scanned by the alternating dual colors, could be used to determine the direction and size of the flow field and thus finish the 2-D velocity measurement by distinguishing different images taken at different time. The continuous Argon ion laser (1) was inexpensive though it had limits in the range and accuracy of measuring velocity. And the combined beam, used in the Alternating Dual Color Image Velocity Measurement, was produced by Argon ion laser (1) which was Low-Cost equipment. However, the wavelength of the laser beam had to be transformed through particular AV modulation techniques, and the special AOM (Acousto-Opto Modulator) was difficult in manipulation and controlling, and even in acquisition.

[0007] The inventor of the Low-Cost Continuous Laser DPIV (Digital Particle Image Velocimetry) has been engaged in observing and measuring flow fields for years and had personally done all the above said methods. It is assured that the Color Alternating Image applied in image velocity measurement can determine the velocity and direction of a flow field rather accurately and effectively. And even more, it may also be applied in biological and micro-mechanical technologies in measuring the transmitting speed in non-intrusive media. To get rid of the above-said manipulating, controlling and acquiring difficulties, the Inventor discard the particular AV modulation techniques to transform combined beams into color alternating beams. Instead, Here is the A Low-Cost Continuous-Wave-Laser (CW Laser) Digital Particle Image Velocimetry and equipment conceived by the inventor.

SUMMARY OF THE INVENTION

[0008] The primary purpose of the invention disclose the Low-Cost Continuous Laser DPIV (Digital Particle Image Velocimetry), which can transform combined beams into color alternating plane beams via certain color alternating producers to diagnose flow fields. And the color alternating images taken by the CCD (Charge Couple Device) can be analyzed by a PC (personal computer), and with the help of cross-correlation analysis method, determine the size and direction of a flow speed.

[0009] The other purpose of the invention disclose a Low-Cost Continuous-Wave-Laser (CW Laser) Digital Particle Image Velocimetry that can determine the velocity and its direction of a particle, its moving locus, the velocity in a 2-D plane and the velocity distribution in a 3-D space via PC (personal computer) processed images taken by the CCD (Charge Couple Device) in particle flow fields.

[0010] While the invention is susceptible to various modification and alternative forms, certain illustrative embodiments thereof have been shown by way of example in the drawing and will herein be described in detail.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The invention will now be described by way of example with reference to the accompanying Tables and Figures in which:

[0012] FIG. 1: Separation of Image Signal & Application of “cross-correlation analysis method”

[0013] FIG. 2: Low-Cost Continuous Wave Digital Laser Particle Velocity Meter

[0014] FIG. 3: color alternating plane beam producer

[0015] FIG. 4: Intermittent Beam Chopper

REFERENCE NUMBER OF THE ATTACHED DRAWINGS

[0016] 1 . . . Argon ion laser

[0017] 2 . . . Combined Output of Multi-wave & Multi-color Beams

[0018] 3 . . . color alternating plane beam producer

[0019] 4 . . . intermittent green light pulses

[0020] 5 . . . blue and green plane beams

[0021] 6 . . . CCD (Charge Couple Device) Trigger

[0022] 7 . . . Signal Cable

[0023] 8 . . . CCD (Charge Couple Device)

[0024] 9 . . . PC (personal computer)

[0025] 25 . . . Color Alternating Plane Beam

[0026] 31 . . . Bypass Spectroscope

[0027] 51 . . . Particle Flow Field

[0028] 71 . . . TTL (Standard 5 V Square-wave) Signal

[0029] 81 . . . Lead

[0030] 101 . . . digital color photo

[0031] 102 . . . green beam image

[0032] 103 . . . Blue Image

[0033] 104 . . . Image Color Separation

[0034] 105 . . . Cross-relation Analysis

[0035] 106 . . . Particle Moving Speed

[0036] 301 . . . Beam Splitter

[0037] 302 . . . Green

[0038] 303 . . . Blue

[0039] 304 . . . Plane Reflector

[0040] 305 . . . Intermittent Beam Chopper

[0041] 306 . . . Green Intermittent Beam Pulse

[0042] 307 . . . Blue Intermittent Beam Pulse

[0043] 309 . . . Beam Combinator

[0044] 310 . . . Plane Beam Scatterer

[0045] 311 . . . Photomultiplier Tube

[0046] 312 . . . Signal Producer Controller

[0047] 3051 . . . Variable Motor

[0048] 3052 . . . Multi-opening Beam Chopper Plate

[0049] 3053 . . . Set 1 openings

[0050] 3054 . . . Set 2 openings

[0051] 3055 . . . Set 3 openings

DETAILED DESCRIPTION OF THE INVENTION

[0052] The equipment used in the A Low-Cost Continuous-Wave-Laser (CW Laser) Digital Particle Image Velocimetry of the invention, is a set of Beam Splitter (301) for separating combined laser beams and a Intermittent Beam Chopper (305) for respectively and intermittently stopping the separated laser beams in order to produce two alternating intermittent beams. When going through a Beam Combinator (309) and then a Column Prism, these two intermittent beams will scatter into color alternating plane beams (25). After processed by a PC (personal computer, 9) for color separation with the help of cross-correlation analysis method (105), images taken by the CCD (Charge Couple Device) in a particle flow field (51) scanned by such plane beams can be used to determine a particle's velocity and direction in a 2-D measurement. All the equipment necessary for the velocity measurement A Low-Cost Continuous-Wave-Laser (CW Laser) Digital Particle Image Velocimetry are most primary and inexpensive optical components and parts especially improved for use in flow fields (like Argon ion laser (1), optical prisms, etc.). Apparently, such equipment is both inexpensive and competitive in markets.

[0053] The DPIV (Digital Particle Image Velocimetry) equipment includes:

[0054] a Argon ion laser (1);

[0055] a color alternating plane beam producer (3),

[0056] a Bypass Spectroscope (31)

[0057] CCD (Charge Couple Device, 8)

[0058] PC (personal computer, 9)

[0059] Intermittent Beam Chopper (305); and

[0060] a Plane Beam Scatterer (310)

[0061] The feature of such equipment is its unique configuration: a plane reflector (304) installed behind color alternating plane beam producer (3) to adjust beams going into the Intermittent Beam Chopper (305); a plane reflector (304) installed behind the Intermittent Beam Chopper at different distances to lead beams into the Beam Combinator (309); and, at last, a Plane Beam Scatterer (310) is installed behind the Beam Combinator (309). Besides, CCD (Charge Couple Device) Trigger (6) is mounted after and aligned to the axis of the Bypass Spectroscope (31).

[0062] The Intermittent Beam Chopper (305) includes a Variable Motor (3051), and a Multi-opening Beam Chopper Plate (3052) that has two circumferences designed, inner and outer. On each circumference, there are three sets of openings drilled as required, with the same number but different specifications.

[0063] The equipment used Argon ion laser (1) in the A Low-Cost Continuous-Wave-Laser (CW Laser) Digital Particle Image Velocimetry of the invention, whether have color alternating plane beam producer (3) before the laser axis, a Bypass Spectroscope (31) at the side of color alternating plane beam producer (3) to receive part of intermittent green light pulses (4), and CCD (Charge Couple Device) Trigger (6) behind the axis of the Bypass Spectroscope (31). CCD (Charge Couple Device) Trigger is connected to the CCD (Charge Couple Device, 8) with a Signal Cable and the signals of the CCD (Charge Couple Device) is sent to a PC (personal computer, 9 ) with a lead (81).

[0064] The equipment of color alternating plane beam producer (3), shown as FIG. 3; two plane reflector (304) installed behind the Beam Splitter (301) to adjust two beams going into the Intermittent Beam Chopper (305); a plane reflector (304) installed behind the Intermittent Beam Chopper (305) at different distances to lead beams into the Beam Combinator (309) whether consisting of two pentagonal prisms; and a Plane Beam Scatterer (310) made of a common column prism, that behind Beam Combinator (309).

[0065] The Continuous Laser DPIV (Digital Particle Image Velocimetry) has a Bypass Spectroscope (31) whether installed between the Intermittent Beam Chopper (305) and the Plane Reflector (304), and CCD (Charge Couple Device) Trigger (6) behind the axis of the Bypass Spectroscope (31). CCD (Charge Couple Device) Trigger (6) is connected to the CCD (Charge Couple Device, 8) with a Signal Cable whether consists mainly of a Photomultiplier Tube (311), a Photomultiplier Tube Power Supply and a Signal Producer Controller.

[0066] The above-said Intermittent Beam Chopper (305) is shown as FIG. 4, that includes a Variable Motor (3051) and a Multi-opening Beam Chopper Plate (3052). The Plate has two circumferences designed, inner and outer. On each circumference, there are three sets of openings drilled as required, with the same number but different specifications. Among the three sets of openings, said Set 1 openings (3053), Set 2 openings (3054), Set 3 openings (3055). The Set 1 openings (3053) and Set 3 openings (3055) are radial, Set 1 openings (3053) and Set 2 openings (3054) are both at the outer circumference, and Set 2 openings (3054) and Set 3 openings (3055) are radial and arrayed alternatively.

[0067] The determine method of particle velocity and its direction apply Low-Cost Continuous-Wave-Laser (CW Laser) Digital Particle Image Velocimetry, that is illustrated in FIGS. 2, 3, and 4 in sequence. of the Low-Cost Continuous Laser DPIV (Digital Particle Image Velocimetry) Multi-wavelength and Multi-color beams (2), output from Argon ion laser (1) of a Continuous Laser DPIV (Digital Particle Image Velocimetry), which can output such kind of beams continuously, are combined beams in which blue beams (488 nm) and green beams (514.5 nm) are the most intensive.

[0068] As the laser-combined beams enter color alternating plane beam producer (3), and go through all the devices shown in FIG. 3, will produce alternating blue and green plane beams (5) to illuminate a particle flow field (51). Besides, there is a Bypass Spectroscope (31) installed inside color alternating plane beam producer (3) that can bypass part of the intermittent green light pulses (4), through the Photomultiplier Tube (311) and the Signal Producer Controller CCD (Charge Couple Device) Trigger (6), to the CCD (Charge Couple Device) Trigger (6).

[0069] As the Trigger receives a green laser signal, it will immediately output a standard TTL (71) whether have standard 5 V square wave, via a signal cable (7) to the CCD (Charge Couple Device, 8), through the signal can actuate the shotter to take images and record data of the streamlines' geometrical distributions, such as the shape of the flow field, the velocity and Turbulence, etc. in a particle flow field (51). And the digital color images taken will be sent right away via a lead (81) to a PC (personal computer, 9) with photo processing interface for storage. Through the process illustrated in FIG. 1, a color separation treatment of the CCD (Charge Couple Device, 8) images will be done to determine the velocity and direction of a particle, its moving locus, the 2-D velocity in the flow field, and the velocity distribution in a 3-D space.

[0070] FIG. 3 shows the process of laser combined beams producing blue and green plane beams (5) to illustrate a particle flow field (51). While Combined Output of Multi-wavelength Multi-color beams (2), output from a laser, go into color alternating plane beam producer (3), they will first enter the Beam Splitter (301) consisting of dual equilateral triangular column prisms and thus blue and green beams will be separated away from the combined beams, forming two continuous blue (302) and green (302) beams that have their own respective courses. It is the same way as the sunlight is separated into red, orange, yellow, green, blue, indigo, and violet while going through a Beam Splitter. To reduce the room for beam trips when configuring the optical equipment, plane reflectors (304) are needed to adjust the beams in order to take the most advantages of the room. These two reflectors, in addition, have to adjust the two beams going parallel to each other into the Intermittent Beam Chopper (305) which device as shown in FIG. 4. As the blue (302) and green (303) continuous laser beams go parallel into the Chopper, they will respectively become intermittent alternating beam pulses: said one is green Intermittent Beam Pulse (306) and the other blue Intermittent Beam Pulse (307), when one goes, the other stops. Then again adjusted by two plane reflectors (304), the green and blue intermittent alternating beam pulses will go parallel into the Beam Combinator (309), forming a color-alternating beam. The Beam Combinator (309), composed of two pentagonal prisms, can make the two intermittent beam pulses combine into one color-alternating beam since different color beams have different refraction indices while passing through a quartz glass. Light may either refract or reflect, depending on its refraction index. Taking advantages of this feature, we can make the two parallel intermittent beam pulses going to the dame course and thus combining into one beam.

[0071] The shotter is actuated by TTL (standard 5 V square waves) signals. The output of such signals is activated when the CCD Trigger (6) receives bypassing green intermittent beam pulses. To achieve the above purpose, a Bypass Spectroscope (31) is installed in the course of the intermittent green beam pulses (306), and transfer intermittent green beam pulses (306) to intermittent green light pulses (4). As the intermittent green light pulses (4) go through the Bypass Spectroscope (31), it will be led to CCD (Charge Couple Device) Trigger (6), which consists mainly of a Photomultiplier Tube (311), a Photomultiplier Tube Power Supply and a Signal Producer Controller.

[0072] As shown in FIG. 4, when the Multi-opening Chopper Plate (3052) of the Intermittent Beam Chopper (305) is being driven by a speed variable motor (3051), openings of Set 2 (3054) and Set 3 (3055) will alternatively and also intermittently stop the blue and green beams, and make them become alternating intermittent beam pulses (when one goes, the other stops). Set 1 openings (3153), as a reference to Set 2 openings (3154), are used to monitor the rotation speed of the speed fixed motor. After the Beam Chopper, a Beam Combinator (309) is installed to combine the two alternating intermittent beam pulses into a color-alternating beam; and then this color-alternating beam will transform into a color-alternating plane beam by a Plane Beam Scatterer (310). The frequency of the alternating beam pulses can be adjusted by the Rotating Speed Controller of the Motor.

[0073] As the invention “Method & Equipment of the Low-Cost Continuous Laser Digital Particle Image Velocity Measurement” uses a Photomultiplier Tube to sense a single color beam to actuate the CCD (Charge Couple Device), the alternating times (i.e. the pulse frequency) and order of the blue and green beams can be inferred. In such a way, the quality of images taken is assured.

PRACTICAL OPERATION PROCEDURE

[0074] 1. Produce a combined beam of blue and green by Argon ion laser (1).

[0075] 2. Separate the combined beam into two single blue and green beams by using coupled equilateral hexagonal prisms as a set of Beam Splitter.

[0076] 3. Mount a reflector at a proper position to reflect the blue and green beams, letting the green beam above and parallel to the blue.

[0077] 4. As the two beams vertically go through the openings of the rotating “Multi-openings Beam Chopper Plate (3052),” with the green beam passing through the inner Set 3 openings and the blue beam through the outer Set 2 openings, pulses of intermittent blue and green beams are made since the beams can only go past the openings and will be stopped by the plate.

[0078] 5. Mount a reflector at a proper position to reflect the two beam pulses, parallel to each other.

[0079] 6. Equip a Bypass Spectroscope (31) in the course of the intermittent green beam pulsess between the Multi-opening Beam Chopper Plate (3052) and the reflector to lead part of the green beam into a Photomultiplier Tube (311).

[0080] 7. Combine the two parallel beam pulses into a color-alternating beam with a Beam Combinator.

[0081] 8. Use a column prism as a Plane Beam Scatterer to scatter the color-alternating beam into color-alternating plane beams, which will be led to the particle flow field (51) for measurements.

[0082] 9. As the Photomultiplier Tube (311) catches the intermittent green light pulsess, the controller of the Photomultiplier Tube will immediately output a TTL signal to the CCD (Charge Couple Device) Trigger (6) unit, actuate the shutter and thus begin taking images.

[0083] 10. Process the images on a PC (personal computer, 9), and with the help of cross-correlation analysis method, determine particles' directions and speeds in the flow field.

[0084] From the above practical operation, we understand that the “Low-Cost Continuous Laser DPIV (Digital Particle Image Velocimetry)” only needs basic equipment often used in flow field measurement, in addition to color alternating plane beam producer (3). With such simple equipment-Low-Cost and easily operating, many complicated 2-D flow-field velocity measurement can be easily and inexpensively completed.

Claims

1. A continuous laser DPIV (Digital Particle Image Velocimetry), whether including: Argon ion laser color alternating plane beam producer Bypass Spectroscope CCD (Charge Couple Device) PC (personal computer) Intermittent Beam Chopper Plane Beam Scatterer The feature of such equipment is its unique configuration: a plane reflector installed behind color alternating plane beam producer to adjust beams going into the Intermittent Beam Chopper; a plane reflector installed behind the Intermittent Beam Chopper at different distances to lead beams into the Beam Combinator; and, at last, a Plane Beam Scatterer is installed behind the Beam Combinator. Besides, CCD (Charge Couple Device) Trigger is mounted after and aligned to the axis of the Bypass Spectroscope. The Intermittent Beam Chopper includes a Variable Motor, and a Multi-opening Beam Chopper Plate that has two circumferences designed, inner and outer. On each circumference, there are three sets of openings drilled as required, with the same number but different specifications.

2. The continuous laser DPIV (Digital Particle Image Velocimetry) according in claim 1, the equipment of the Continuous Laser DPIV includes a continuous laser, color alternating plane beam producer before the laser axis, a Bypass Spectroscope at the side of color alternating plane beam producer to receive part of intermittent green light pulses, and CCD (Charge Couple Device) Trigger behind the axis of the Bypass Spectroscope. CCD Trigger is connected to the CCD with a Signal Cable and the signals of the CCD is sent to a PC (personal computer) with a lead.

3. The continuous laser DPIV (Digital Particle Image Velocimetry) according in claim 1, the Continuous Laser DPIV has two Plane Reflectors installed behind the Beam Splitter to adjust the two beams going parallel into the Intermittent Beam Chopper, two Plane Reflectors installed at different distances behind the Chopper to lead beams parallel entering the Beam Combinator, and a Plane Beam Scatterer behind the Combinator.

4. The continuous laser DPIV (Digital Particle Image Velocimetry) according in claim 1, the Continuous Laser DPIV has a Bypass Spectroscope installed between the Intermittent Beam Chopper and the Plane Reflector (near end), and CCD (Charge Couple Device) Trigger behind the axis of the Spectroscope. CCD Trigger is connected to the CCD with a Signal Cable.

5. The continuous laser DPIV (Digital Particle Image Velocimetry) according in claim 1, the Intermittent Beam Chopper of the Continuous Laser DPIV includes a Variable Motor and a Multi-opening Beam Chopper Plate. The Plate has two circumferences designed, inner and outer. On each circumference, there are three sets of openings drilled as required, with the same number but different specifications. Among the three sets of openings, Set 1 openings and Set 3 are radial, Set 1 openings and Set 2 are both at the outer circumference, and Set 2 openings and Set 3 are radial and arrayed alternatively.