Mutual diffusion process for continuousfabrication of graded-index plastic rod lenses

Yoshihiro Uozu and Kazuyuki Horie

We propose a new process for fabrication of plastic rod lenses based on the traditional method of fiberextrusion. The process consists of the following steps: multilayer conjugate extrusion, monomer dif-fusion between adjacent layers, and photopolymerization of an uncured strand fiber. We call thisprocess a mutual diffusion process for continuous plastic rod lens fabrication. Characteristics of thisprocess are as follows: fast production speed ��100 cm�min�, precision control of refractive-indexdistribution, high angular aperture, and long-term reliability. The optical resolution of the rod-lensarray is 300 dpi, which is high enough for application to G3 facsimiles with transmission time of less than1 min and monochromatic scanners. © 2003 Optical Society of America

OCIS codes: 110.2760, 160.5470, 220.4610, 110.4100, 350.3950.

1. Introduction

A rod lens is a cylindrical lens that has a graded-index distribution in the radial direction. Because asinusoidal light path is formed along the center axisof the lens, one can obtain erect real images for ap-propriate lens lengths, as shown in Fig. 1. Usuallyrod lenses are arrayed in the form of a single row orin dual rows. A reading sensor head with a linearrod lens array is a typical application device thatscans a wide area to read two-dimensional informa-tion. Linear rod lens arrays have many applica-tions, such as facsimiles, image scanners, copymachines, and LED printers. Rod lens arrays havetraditionally been made only from glass.1 Fabrica-tion of plastic rod lenses has been tried by severalauthors,2–6 but many problems needed to be solved:insufficient resolution, lack of uniformity inrefractive-index distribution, poor chemical andphysical durability, and lack of facilities for produc-tion on an industrial scale.

In the past decade we also attempted to fabricateplastic rod lenses, especially by a continuous pro-

Y. Uozu �uozu_yo@mrc.co.jp� and K. Horie are with the Depart-ment of Organic and Polymer Materials Chemistry, Tokyo Univer-sity of Agriculture and Technology, Naka-cho, Koganei, Tokyo 184-8588, Japan. Y. Uozu is also with the Corporate ResearchLaboratories, Mitsubishi Rayon Company, Ltd., 20-1 Miyuki-cho,Ohtake, Hiroshima 739-0693, Japan.

Received 8 November 2002; revised manuscript received 14 July2003.

0003-6935�03�316342-07$15.00�0© 2003 Optical Society of America

6342 APPLIED OPTICS � Vol. 42, No. 31 � 1 November 2003

cess. Recently we developed a new continuous pro-duction process to make plastic rod lenses with highquality and good durability commercially avail-able.7,8 We call it a mutual diffusion process forcontinuous fabrication of plastic rod lenses. Inthis paper we present the basic concept and exper-imental results of our evaluation of new fabricationprocess.

2. Mutual Diffusion Process

First we describe this technique. The concept of mu-tual diffusion for continuous fabrication of plastic rodlenses is illustrated in Fig. 2. We can describe thisprocess as follows:

�1� Several uncured polymer-in-monomer mixtures�a number N � 2 of mixtures with different refractiveindices nD� are prepared. Polymer A is dissolved inseveral monomers, B1, B2, . . . , Bi, each of which hasa different refractive index from that of polymer Aand from the other B polymers. Each uncured mix-ture has different constituents of monomers andhence has a different nD. These uncured mixturesare concentrically laminated; they are extruded froma concentric combination nozzle, thereby forming anuncured multilayer strand fiber.

�2� Monomers are then mutually diffused betweenadjacent layers to provide a continuous refractive-index distribution.

�3� During diffusion or thereafter, the uncuredstrand fiber is cured.

For inner layers, monomers with higher refractiveindices �e.g., benzyl methacrylate, phenyl methac-rylate� are used, and for outer layers monomerswith lower refractive indices �e.g., fluoroalkylmethacrylate� are used. In this technique a widerefractive-index range can be achieved owing to mu-tual diffusion of monomers with higher and lowerrefractive indices, which is different from the utili-zation of one-way diffusion in conventional tech-niques. Accurate regulation of refractive-indexdistribution can be achieved by control of manyoperational factors: composition of each layer;thickness of each layer; temperatures at the conju-gate nozzle, the diffusion area, and the photopoly-merization area; and intensity of UV light. Precisecontrol of these factors results in uniformity of in-dividual lenses during continuous production; thussetting the plastic rod lens arrays into image sensormodules has become easier than for glass lens ar-rays, which are produced in a batch system andhence exhibit gradient constants that vary amongbatches.

3. Experiment

A. Production of Plastic Rod Lens

We describe here experiments for production of plas-tic rod lenses with five layers.

A mixture consisting of 34.65 wt. % benzyl methac-rylate, 13 wt. % methyl methacrylate, 0.25 wt. %1-hydroxycyclohexylphenylketone, 0.1 wt. % hydro-quinone, and 52 wt. % poly�methyl methacrylate� ����� 0.40 dL�g� 52 was kneaded at 70 °C and consti-tuted the first layer. Next, a mixture consisting of9.65 wt. % benzyl methacrylate, 35 wt. % methylmethacrylate, 7 wt. % 2,2,3,3,4,4,5,5-octafluoropentylmethacrylate, 0.25 wt. % 1-hydroxycyclohexyl phe-nylketone, 0.1 wt. % hydroquinone, and 48 wt. %poly�methyl methacrylate� ���� � 0.40 dL�g� waskneaded at 70 °C and served as the second layer. Amixture consisting of 30 wt. % methyl methacrylate,22.65 wt. % 2,2,3,3,4,4,5,5-octafluoropentyl methac-rylate, 0.25 wt. % 1-hydroxycyclohexylphenylketone,0.1 wt. % hydroquinone, and 47 wt. % poly�methylmethacrylate� ���� � 0.40 dL�g� kneaded at 70 °Cbecame the third layer. A mixture consisting of18 wt. % methyl methacrylate, 41.65 wt. %2,2,3,3,4,4,5,5-octafluoropentyl methacrylate, 0.25wt. % 1-hydroxycyclohexylphenylketone, 0.1 wt. %hydroquinone, and 40 wt. % poly�methyl methacry-late� ���� � 0.40 dL�g� was kneaded at 70 °C andformed the fourth layer. Lastly, a mixture consist-ing of 4 wt. % methyl methacrylate, 58.65 wt. %2,2,3,3,4,4,5,5-octafluoropentyl methacrylate, 0.25wt. % 1-hydroxycyclohexylphenylketone, 0.1 wt. %hydroquinone, and 37 wt. % poly�methyl methacry-late� ���� � 0.40 dL�g� kneaded at 70 °C became thefifth layer.

A combination nozzle with several �1 � N� concen-tric plates was used, and the first layer was put in thecenter of the spindle, the second layer was placed inan adjacent outer position, and so on. A filamentthat comprised several layers was formed from thecombination nozzle kept at 42 °C, and the radialthickness ratio of the five layers was 36�37�20�6�1.Next, the filament was sent to a 30-cm-long diffusionsection maintained at 40 °C, where monomers dif-fused between layers spontaneously. Then the fila-ment was sent to a 120-cm-long photopolymerizationsection that had 18 40-W chemical lamps at 40 °C,where the monomers were polymerized and also dif-fused between layers spontaneously. Then the fila-ment was sent to the last section to finishphotopolymerization with three high-pressure 2 k-Wmercury lamps. In these sections, nitrogen gas waspassed through the apparatus at the rate of 70 L�minand the filament was sent at a rate of 50 cm�min.

In this way we produced a plastic rod lens withhigh performance.

B. Production of the Rod Lens Array

Rod lenses were placed in a single row, in dual rows,or in several rows between two parallel black sub-strates. An adhesive with a shading agent such ascarbon black filled the gaps between lenses and base

Fig. 1. Schematic of image transfer through a rod lens: P, pitchof the light oscillating about the axis of the rod lens.

Fig. 2. Mutual diffusion process for continuous fabrication ofplastic rod lenses.

1 November 2003 � Vol. 42, No. 31 � APPLIED OPTICS 6343

plates, and then the assembly was rigidified. Sub-sequently this lens array was cut into the desiredlengths, and then the mirror-finished surfaces of theend faces were polished with a diamond blade.

C. Imaging Method for Evaluation of Lenses

Figure 3 shows an apparatus for measuring deformedimages. The deformed image of a test pattern wasrelated to the performance of the rod lenses byYamamoto and Iga.9 To measure the sizes of theaberrations we employed a mesh with constant lineintervals of 0.1 mm as a pattern to be observedthrough the sample lens. The mesh was irradiatedwith a helium–neon laser �633 nm�. Figure 4 illus-trates various images. A good performance lens hasan image with no distortion �Fig. 4�b��, and a badperformance lens shows either a barrel distortion�Fig. 4�a�� or a pincushion distortion �Fig. 4�c��.

D. Modulation Transfer Function

We employ a modulation transfer function �MTF� toevaluate the resolution of linear rod lens arrays.10,11

The MTF expresses quantitatively the degree of pre-cision of the image through a lens array. The equip-ment for measuring a MTF is shown schematically inFig. 5. The light source is a halogen lamp with amonochromatic filter and a diffusing plate, whichprovides incident light at a given wavelength. A testchart with lines and spaces follows the diffusing plateto give the spatial frequency. The MTF of lens ar-rays at a given spatial frequency �W line pairs �lp��

mm� is calculated in a simple manner with thefollowing equation:

MTF�W� �I�W�max � I�W�min

I�W�max � I�W�min� 100�%� (1)

where I�W�max and I�W�min are the maximum andminimum values, respectively, of the light intensityof the image at a given spatial frequency, W �lp�mm�.A higher value of the MTF corresponds to better per-formance of the rod lens array.

4. Results and Discussion

A. Optical Characteristics of the Plastic Rod Lens

Figure 6 shows the image of a plastic rod lens pre-pared under the conditions described above and mea-sured with the imaging method. No distortion wasobserved in the image. Figure 7 shows therefractive-index distribution relative to radial dis-tance from the center axis of a plastic rod lens with a0.47-mm radius measured with an interference mi-croscope.12 The observed values are plotted as filledsquares, and the solid curve corresponds to the valuesaccording to the following approximate expression12:

n�r� � n0�1 � g2r2�2�1�2, (2)

Fig. 3. Apparatus for measuring deformed images.

Fig. 4. Various images through rod lenses.

Fig. 5. Equipment for measurement of MTF.

Fig. 6. Image through the plastic rod lens.

6344 APPLIED OPTICS � Vol. 42, No. 31 � 1 November 2003

where r is the distance from the center axis, n�r� isthe refractive index at r, n0 is the refractive index atthe center axis, and g is the gradient constant.

The refractive-index distribution of the rod lenssubstantially agreed with the ideal refractive-indexdistribution curve approximated by Eq. �2� over theradial distance from the center axis to 80% of itslength �420 �m�. The refractive-index distributionnear the surface deviates appreciably from the idealrefractive-index distribution curve.

The optical characteristics of the plastic rod lensare as follows: The emitting angle is 22.7°, the di-ameter of the lens is 0.93 mm, and gradient constantg is 0.564 mm1, which is slightly larger than the

value previously reported.4–6 The pitch of the rodlens, P � 2�g, is 11.1 mm.

B. Optical Characteristics of the Plastic Rod Lens Array

Figure 8 illustrates the structure and dimensions ofthe lens arrays fabricated here. Typical values ofoptical and physical parameters of the lens arrays areas follows: The measuring wavelength was 570 nm.When the length of the lens array was 6.6 mm, thetotal conjugate length was 14.4 mm. After measur-ing MTF values at several total conjugate lengths, wedetermined the optimum total conjugate length atthe highest MTF value in this lens array. The high-est MTF value of the lens array at 4 lp�mm was 68%.

MTF values for the plastic rod lens array and thestandard grade of glass rod lens arrays �SLA20B� atseveral spatial frequencies are summarized in Table1. At each spatial frequency the MTF value for theplastic rod lens array is only 10% less than that of theglass rod lens array.

C. Influences of Several Spinning Conditions on OpticalCharacteristics

1. Temperature of the Combination NozzleFirst we determined the effects on the optical char-acteristics of the plastic rod lens when we changedonly the temperature of the combination nozzle underthe conditions of lens production described above; theresults are listed in Table 2. The MTF value wasmaximum at 42 °C, and an image with no distortionwas obtained.

When the temperature of the nozzle becamehigher, the image pattern began to show the barrel-

Fig. 7. Refractive-index distribution of the plastic rod lens:filled squares, experiment; solid curve, fit according to Eq. �2� withg � 0.564 mm1.

Fig. 8. Structure and dimensions of the rod lens array.

Table 1. MTF Values for the Plastic Rod Lens Array and aStandard-Grade �SLA20B� Glass Rod Lens Arraya

Spatial Frequency�lp�mm�

MTF �%�

Plastic RodLens Array

Glass RodLens Array

4 70 826 64 788 57 70

awavelength, � � 570 nm.

Table 2. Optical Characteristics of the Plastic Rod Lens Relative to Temperature at the Conjugate Nozzle

Property

Run Number

1 2 3 4 5

Temperature at the nozzle �°C� 40 42 44 46 48MTF at 4 lp�mm �%� 61 68 64 58 42Gradient constant, g �mm1� 0.568 0.564 0.560 0.555 0.548Image through rod lens

1 November 2003 � Vol. 42, No. 31 � APPLIED OPTICS 6345

type distortion. Then the MTF value of the lensarray deteriorated and the conjugate length of thearray increased, too. In addition, when the nozzletemperature became low, the image pattern was ofthe pincushion type, the MTF deteriorated, and theconjugate length of the array shortened.

When the nozzle temperature became higher,monomer diffusion between layers proceeded too fast.So the refractive index at the center axis becamelower, the refractive index at the outer portion be-came higher, and gradient constant g becamesmaller. The change in lens characteristics de-scribed above occurred as the result.

2. Temperature of the Diffusion SectionNext we examined the influence of the temperature ofthe diffusion section on the optical characteristics ofthe plastic rod lens with the other conditions of lens

production maintained the same as described above.The results are given in Table 3.

When the temperature of the diffusion section be-came higher, the image pattern began to show barreldistortion. Then the MTF value of the lens arraydeteriorated, and the conjugate length of the arrayincreased, too. In this case, because of heat radia-tion from the apparatus we could not keep the tem-perature of the diffusion section below 35 °C and wecould not carry out experiments at temperatureslower than 40 °C.

When the diffusion section temperature becomeshigher, monomer diffusion between layers proceedsmore rapidly. So the refractive index at the centeraxis becomes lower, the refractive index at outerparts becomes higher, and then gradient constant gbecomes smaller. The change in lens characteristicsdescribed above can be observed as a result.

3. Radial Thickness Ratio of Five LayersWe also examined the influence on the optical char-acteristics of the plastic rod lens when we changedonly the radial thickness ratio of the five layers in thelens-production procedure described above. The re-sults are given in Table 4.

The refractive indices of the first-, second-, third-,fourth-, and fifth-layer polymer blends, when theywere photopolymerized independently, were 1.518,1.493, 1.472, 1.456, and 1.440, respectively. How-

Table 3. Optical Characteristics of the Plastic Rod Lens Relative to Temperature at the Diffusion Section

Property

Run Number

1 2 3 4

Temperature of the diffusionsection �°C�

40 45 50 55

MTF at 4 lp�mm �%� 68 62 55 45Gradient constant, g �mm1� 0.564 0.561 0.556 0.551Image through rod lens

Table 4. Optical Characteristics of the Plastic Rod Lens Relative to Radial Thickness Ratios of the Five Layers

Property

Run Number

1 2 3 4 5

Radial thickness ratio of thefive layers

36�39�18�6�1 35�37�20�6�1 36�37�20�6�1 37�36�20�6�1 36�35�22�6�1

MTF at 4 lp�mm �%� 56 57 68 58 59Gradient constant, g

�mm1�0.555 0.554 0.564 0.570 0.569

Image through rod lens

Table 5. Durability Tests for the Plastic Rod Lens Arraya

Test Conditions

Heat and humidity 60 °C, 95% relative humidity, 1000 hLow temperature 40 °C, 1000 hHigh temperature 80 °C, 1000 hHeat cycle 80 °C, 30 min; 30 °C, 30 min; 100 cycles

aIn all cases, the conditions of the test caused no change indurability of the lenses.

6346 APPLIED OPTICS � Vol. 42, No. 31 � 1 November 2003

ever, Fig. 7 shows that the refractive index at thecenter axis of the rod lens is 1.510 and that the lowestvalue of the refractive index near the surface is 1.461.The refractive index in the center axis is smaller thanthat for a photopolymerized blend of the first layer.The radial thickness ratio of the five layers is 36�37�20�6�1 from inside to outside, and the diameter of therod lens is 940 �m. The inner position of the thirdlayer is 343 �m in radial distance, the outer positionis 437 �m, and the center position is 390 �m. Figure7 also shows that the refractive indices of inner po-sition, outer position, and center position of the thirdlayer are 1.480, 1.466, and 1.472, respectively. Therefractive index of the inner position is higher thanthe value for the photopolymerized blend of the thirdlayer. These results suggest that monomers in factdiffuse through the neighboring layers. Table 4shows that when the radial thickness ratio of the firstlevel increases, the refractive index of the center axisincreases and the gradient constant increases. Theincrease in radial thickness ratio of the third layer fora constant radial thickness ratio �36� of the first layer�runs 1, 3, and 5� also provides the increase in thegradient constant. However, the refractive-indexdistribution deviates from the ideal curve, and theresolution of a lens falls. The rod lens does not forman image when the radial thickness ratio of thefourth or fifth layer is varied greatly. The optimumradial thickness ratio was determined to be 36�37�20�6�1, as suggested by the mesh images in Table 4.

D. Durability Tests

Finally, we measured the durability of the rod lensarrays by performing several tests under various con-ditions: a heat resistance test �80 °C for 1000 h�, aheat and humidity test �60 °C at 95% relative humidityfor 1000 h�, a low-temperature test �40 °C for 1000 h�,and a heat cycle test �80 °C for 30 min and 30 °C for30 min; 100 cycles�. In these tests the MTF value at4 lp�mm of the lens array hardly changed. We ob-served no change in physical and optical propertiesunder the given conditions. The durability of the rodlens array was sufficient for practical use �Table 5�.

In results reported previously, the lens character-istics varied in durability �especially in heat and hu-midity tests� because compounds of low molecularweight, e.g., solvents, monomers, and dopants usedfor forming the refractive-index distribution, re-mained in the rod lenses. With the present tech-nique we could accomplish substantially completepolymerization of monomers with a photopolymeriza-tion initiator. The plastic rod lens has monomers inamounts of less than 0.5 wt. % and a small amount of

residual photoinitiator. Typical values of monomersleft in a rod lens are 0.2 wt. % methyl methacrylate,0.1 wt. % benzyl methacrylate, and 0.1 wt. % octaflu-oropentyl methacrylate �Table 6�. As thus de-scribed, the good durability of the rod lens resultsfrom success in keeping the amount of low-molecular-weight compounds that remain in plastic rod lensextremely low.

5. Conclusions

We have developed a process for continuous fabrica-tion of plastic rod lenses that we call a mutual diffu-sion process for continuous fabrication of plastic rodlenses. A rod lens fabricated by this process hasgood optical performance and high durability. Inthis technique a wide range of refractive indices canbe achieved because of mutual diffusion of monomerswith higher and lower refractive indices, a procedurethat is different from the utilization of one-way dif-fusion that occurs in conventional techniques. Ac-curate regulation of refractive-index distribution canalso be achieved by control of many factors, whichinclude the composition of each layer; the thickness ofeach layer; temperatures at the conjugate nozzle, thediffusion area, and the photopolymerization area;and the intensity of UV light. Precise control ofthese factors results in uniformity of individuallenses, so setting the plastic rod-lens array into animage sensor module is easier than with the glasslens array fabricated by a batch process. There arewidely applicable uses for rod lens arrays, such asfacsimiles, image scanners, copy machines, and LEDprinters. It is hoped that the plastic rod lens can beused widely in these ways.

We are grateful to Yasuteru Tahara and TerutaIshimaru for measuring the MTFs.

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Table 6. Amounts of Residual Monomers in the Plastic Rod Lens

Fabrication Speed�cm�min�

Residual Monomer �wt. %�

Methyl Methacrylate Benzyl Methacrylate Octafluoropentyl Methacrylate Total

80 0.2 0.1 0.1 0.4120 0.4 0.2 0.5 1.1

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