infrared zone-scanning system

Infrared zone-scanning system

Aleksandr Belousov and Gennady Popov

Challenges encountered in designing an infrared viewing optical system that uses a small linear detectorarray based on a zone-scanning approach are discussed. Scanning is performed by a rotating refractivepolygon prism with tilted facets, which, along with high-speed line scanning, makes the scanning gear assimple as possible. A method of calculation of a practical optical system to compensate for aberrationsduring prism rotation is described. © 2006 Optical Society of America

OCIS codes: 230.0230, 040.2480.

1. Introduction

In an IR scanning system, the scanning techniquehas an appreciable effect on a number of parametersthat decide the sensitivity, resolution, packaging, andcost of the system. One-dimensional parallel or push-broom scanning with a long detection array is cur-rently used in most cases to greatly simplify thescanning gear. Notwithstanding this fact, using lin-ear arrays �20 mm long and containing more than200 elements causes manufacturing methods to be-come sophisticated and the cost of the entire IR sys-tem to increase.

In this paper we provide a design and a method ofcalculation for an IR optomechanical system withzone scanning based on small linear detector arraysof the order of 2 mm long.

Similar scanning systems involving two rotatingprisms1 or one prism and an oscillation mirror2 makeit possible to obtain a television-type sweep pattern buthave a disadvantageously complicated scanning gear1

that requires hard synchronization of two prisms ro-tating at different speeds or of a rotating prism and anodding mirror of the sweep frame.2 In the latter case,the restrictions imposed on the camshaft mechanismcause the sweep frame frequency to fall, particularly insevere temperature conditions. These systems operatewith single-element detectors, yielding a spread spot ofthe order of 2 mm.3 When the size of an element is

estimated to be 0.035–0.050 mm, extra compensationfor aberrations is needed. However, Ref. 4 states that“When scanning [using a prism], aberrations increasedramatically and their correction is likely to be im-possible, since their magnitude is not constant and isa function of scanning angle.”

2. System Design

Nonetheless, we have developed an IR scanning sys-tem consisting of a simple two-element lens, a rotat-ing prism, and image-transfer optics, making itpossible to obtain a spread spot similar to an Airydisk. This IR system uses an eight-facet germaniumprism with tilted facets; the line (azimuth) scanningis done by a rotating prism, and the frame scanningis made by facets sloped in pairs.5

The system successively compensates for aberra-tions of the rotating prism through aberration of thelens followed by compensation for residual aberra-tions by means of image-transfer optics.

Figure 1 shows a simplified optical layout of the IRsystem (with a Galilean nozzle and a folding mirrorremoved) in frame [Fig. 1(a)] and line [Fig. 1(b)] scan-ning planes. The numerals are keyed to parts of thesystem and used to describe its method of operation.

The IR system in Fig. 1 consists of lens 1, madefrom two elements: frontal meniscus 2 and afocalmeniscus 3. Field stop 4 is mounted in the real-imageinterval plane of lens 1 (within air space d4, d5).

Entrance pupil D of lens 1 is located in frontal focalplane F1 of frontal meniscus 2 at a distance of �Sp.Prism 5 has tilted facets DG and D�G� [Fig. 1(b)]. Theprism thickness along the optical axis for smallerslope angles � of facets EE� and JJ� is less than thatof greater slope angles (facets DD� and GG�). Animaginary image interval plane passing throughpoint F1� located inside prism 5 is optically conju-gated with stop 4. This plane corresponds to the

The authors are with the Central Design Bureau “Tochpribor”(Precision Instrument), 179A, D. Kovalchuk Street, Novosibirsk630049, Russia. A. Belousov’s e-mail address is [email protected].

Received 4 March 2005; revised 13 September 2005; accepted 15September 2005.

0003-6935/06/091931-07$15.00/0© 2006 Optical Society of America

20 March 2006 � Vol. 45, No. 9 � APPLIED OPTICS 1931

object plane for image-transfer optics. Conjugation isperformed consecutively along the entire plane offield stop 4 to suit current angle � of prism rotationand facet slope angle � (Fig. 2).

Image-transfer optics 6 (Fig. 1) incorporates twocomponents, one for collimating (7) and one for focus-ing (8), and focuses bundles of rays on small lineararray 2y of detector 9. The linear array is locatedparallel to rotation axis OO of prism 5. Shifting offocusing component 8 along the optical axis is usedfor focusing radiation on a fixed detector during as-sembly of the IR system.

For convenience we consider a zone-scanning ap-proach in tracing the inverse rays. Let us assumethat facet slope angle � [Fig. 1(a)] and the angle � ofprism rotation [Fig. 1(b)] are zero. Rays originatingfrom point F of detector 9 pass through image-transfer optics 6 and prism 5, arriving at the center offield stop 4.

Figure 2 is an arrow B [Fig. 1(a)] view of the field stopwith the linear array of the detector positioned for thegiven case [Fig. 2(a)]. When prism the prism is rotated atangle 2�, a zone 2y�� wide will be formed, where 2y isthe length of the linear array and �� is a linear mag-nification of the image-transfer optics in the inverseray trace. However, instead of a television-typeframe, a narrow scanning zone is obtained. In spite ofthis, if the prism facets slope in pairs at angle �1, theimage of the linear array may be displaced in thedirection of the frame sweep to yield a full-formatframe of 2L� � 2l� size [Figs. 2(b) and 2(c)].

Bundles of rays traversing lens 1 (in the inverseray trace) produce an image in object space. A repre-sentation of the field of view in object space is given inFig. 3; the image of linear array A�A� in the plane ofthe field stop [Fig. 2(c)] will be in position D (Fig. 3) inthe object plane because of the reversal.

Axial ray FB [Fig. 1(a)] traversing prism 5 leaves it

Fig. 1. IR system in (a) the frame and (b) the line scanning planes.

Fig. 2. Distribution of scanning zones in the plane of the field stop versus the facet slope angle �i.

1932 APPLIED OPTICS � Vol. 45, No. 9 � 20 March 2006

parallel to itself and, as meniscus 3 is an afocal one,the ray also travels parallel to the optical axis inspace d2 between meniscuses, i.e., is telecentric.Therefore the ray traversing frontal meniscus 2 in-tersects the optical axis at point F1 located at its backfocal plane (in the inverse ray trace) to form angle �in the frame. The same is true for the orthogonalplane where angle � is obtained in the line [Fig. 1(b)].

It should be noted that the location of the entrancepupil in front of the lens is instrumental in optimumconjugation of the optical IR system with a Galileantelescopic arrangement mounted ahead of it and usedfor changing fields of view.

3. Calculation of Structural Components of Frontaland Afocal Menisci

Let us consider the scanning process in detail. Figure1(b) shows the marking of facets of an eight-facetprism. Table 1 presents the values and signs of theslope angles.

In the initial but not in the zero position, when aprism is rotated at an angle ��, facets DD= that haveslope angle �2 are active, and the image of the lineararray is at the origin of zone D (Fig. 3). When prism5 is rotated at angle 2�, this zone is being scanned.Further, facets EE�–JJ�–GG� are successively intro-duced into the ray trace, and scanning of zones E, J,

and G (Fig. 3) takes place. Therefore, in one-halfrevolution of the prism the frame is scanned in zonesD–G. Further rotating the prism will cause the frameto be scanned in the reverse direction, G–D. Thus inone revolution of the prism the frame is scannedtwice, which makes it possible to increase the scan-ning frequency.

Let us take up the design features of the lens basedon calculation of the first and the second paraxial raytraces. The frontal meniscus is made of germaniumand designed to a spherical aberration minimum.Hence, according to Eq. (11.27) of Ref. 6, we maywrite

R1 � 2�2 n��n � 1�f1��n�2n 1�, (1)

R2 � 2�2 n��n � 1�f1��n�2n � 1� � 4, (2)

and at n � 4 (germanium) R1 � f1�, whereas at d1� 0, R2 � 1.5f1�.

Let us consider the design characteristics of theafocal meniscus made of germanium and assume thatthe primary conditions for the first paraxial ray are

�3 � �0, �4 � 0, �5 � 1, h3 � h4 � �0s1 (3)

and for the second paraxial ray are

�3 � 0,

�4 � �3�n �n � 1�y3�nR3 � �n � 1�L�R3,

�5 � 0,

y3 � �L. (4)

Figure 4 shows the ray trace through the afocalmeniscus, given conditions (3) and (4). From Fig. 4 itfollows that the aperture ray within the meniscustravels parallel to the optical axis ��4 � 0� while thefield ray goes parallel to the optical axis before andafter the meniscus ��3 � �5 � 0�. Conceptually, theafocal meniscus is a solid Galilean system mounted inthe inverse ray trace.

In compliance with the Abbe invariant for paraxialrays we may write for surface R3

n��s� � n�s1 � �n� � n��R3. (5)

As s� � ��4 � 0�, then

s1 � �R3��n � 1�, (6)

h3 � h4 � ��0R3��n � 1�, (7)

and, as the meniscus is afocal �� 0�, then

R4�R3 � �0. (8)

One may obtain the values of radii R3 and R4 by

Fig. 3. Distribution of triads of points (configuration) in the fieldof view of the IR system.

Table 1. Values and Signs of Slope Angles

Facet name Slope Angle Object Zone

DD= �2 � 5°25= DEE= �1 � 1°45= EJJ= ��1 � 1°45= JGG= ��2 � �5°25= GD=D ��2 � �5°25= GE=E ��1 � �1°45= JJ=J �1 � 1°45= EG=G �2 � 5°25= D


calculating the second paraxial ray trace. But it iseasier to refer to Eq. (40) of Ref. 7, taking into accountthe signs and symbols, to obtain

R3 � �n � 1�d3��1 � �0�n, (9)

R4 � ��n � 1�d3��1 � �0�n��0. (10)

Besides, from Eq. (32) of Ref. 6 and the using tele-centricity condition, it follows that

s1 � �n � �0�d3��02 � 1�n. (11)

Simultaneous solution of Eqs. (6), (9), and (11) givesa linear magnification of the meniscus:

�0 � �n � 1��2. (12)

The thickness of the afocal meniscus may be foundbased on its afocal condition:

d3 � n�R3 � R4��n � 1�. (13)

Relations (6)–(13) correlate the design componentsof the afocal meniscus.

4. Specific Embodiment of the IR System

The IR zone-scanning system using a rotating prismprovides good image quality at �F�#s�-numbers up to1.7 and fields of view up to 12° (at f � � 100 mm).Mounting an afocal meniscus close to the image in-terval plane enhances the F�# of the IR system forfield bundles of rays and compensates for losses ofimage illumination when the prism is rotated. Raytrace calculations revealed that the F�# enhance-

ment at the edge of the scanning field reached 15%;the reason is that the afocal meniscus introduces abig coma equal in magnitude to that of a prism ro-tated at a working angle, which in turn causes theAbbe sine condition to be disturbed. One may furtherenhance the optical properties of an IR system, suchas angular resolution, field of view, and equivalentF�#, by increasing the length of the lens to someextent to reduce the equivalent F�# of the frontalmeniscus and by using telescopic Galilean nozzles.

Let us now consider a specific embodiment of the IRsystem covering a field of view of 2� � 2� � 6°� 9°, using a linear detector array 1.92 mm long andan eight-facet germanium prism 42 mm thick withtilted facets and a sweep efficiency of 50%, i.e.,� � 11.3°. The size of the detector pixel measures0.035 mm � 0.035 mm.

In this case, as pointed out above, four scanningzones will be generated, each of which corresponds toan angle of 1.5° in the frame. Therefore an equivalentfocal length must be 1.92 mm�tan 1.5° � � 73 mm.

When the prism is rotated at an angle � � 11.3°however, a half-line long;

L� � �n � 1�d6 tan ��n � 6.3 mm (14)

is scanned; i.e., the focal length of the lens will equalf0� � 6.3�tan 4.5° � 78 mm (Fig. 3).

Thus magnification �� of the image-transfer opticswill come to �� 0.935x, while the size of a singlezone in the plane of the field stop will be l��4 �1.92�0.935 � 2 mm.

To obtain an interior zone it should be shifted by1 mm. Consequently the smaller facet slope will be

tan �1 � n�d6�n � 1� � 0.032.

Fig. 4. Trace of (I) the first and (II) the second paraxial rays through afocal meniscus.


To obtain an exterior zone it should be shifted by asmuch as 1 2 � 3 mm. Consequently the bigger facetslope will be

tan �2 � 3n�d6�n � 1� � 0.095.

To prevent object areas from being skipped we take

tan �1 � 0.03, tan �2 � 0.093.

With allowance made for the considerations givenabove, we arrived at an optical layout of the IR sys-tem whose optical characteristics and design featureshave the values given in Tables 2 and 3, respectively.

Figure 3 shows a field of view in object space. Theimage quality is taken up for triads of points 1–18,each composed of 6 configurations. The sequence andnumbers of field points that correspond to each con-figuration are given in Table 4. It will suffice to con-sider the image quality in the first quarter of the fieldof view.

Table 1 gives the values of facet slope angles � thatcorrespond to scanning zones D and G. Configura-tions 1 and 4 match the central area in the directionof frame scanning �� 0�; configurations 2 and 5,zonal area �� 8°�; configurations 3 and 6 fall withinthe edge of the scanning field �� 11.3°�. Zones E andJ correspond to facet slope �1 � �1°45�; zones D andG, to facet slope �2 � �5°25�.

Let us consider the parameters required for calculationof the IR system’s image quality in direct ray tracing. Tothis end, let us have a look at Table 5, where d5 and d7are air space values [Fig. 1(a)], d6 is the prism thick-ness along the axis, � is the angle of the field of viewin the frame for three points of the field (upper, cen-tral, and lower), tan � is the tangent of the facet slopeangle, � is the angle of the field of view in the line forthree points of the field, and tan � is the tangent ofthe prism’s rotation angle.

The values d5, d6, and d7 are not constant and varywith cos �. In addition, to compensate for the fieldcurvature to the frame the prism thickness for con-figurations 1–3, i.e., zones E and J, is 0.2 mm lessthan that for configurations 4–6.

Air spaces d5 and d7 for configurations 1–3 aregreater by 0 and 1 mm, respectively. Note angle �1� � 0.02° for configurations 1–3 and �1 � 1.4° in-stead of �1 � 1.45° for configurations 4–6. This indi-cates some superposition of zones within 1 to 2 pixels.

The linear detector array is � 2 mm long; i.e., coor-dinates of three points of the field (triad) for all con-figurations must have the values �1, 0, and 1 mm.These values are obtained by adjusting values � and� at given � and �.

5. Discussion of Results

Figure 5 shows spot diagrams that include all 18points in the plane traversing point F1�. A scale rule0.5 mm long is provided at the top left. All spots of�0.25 mm diameter are symmetric, suggesting thatcoma has been corrected. In spite of the importantresidual aberrations left, they all have constant mag-

Table 2. Design Features

ItemNumber Radius, R Thickness, d Material

ClearApertureDiameter

1 51.52 6.0 Ge 522 72.44 41.0 503 �11.324 9.0 Ge 184 �18.072 4.0 205 0 6.7 9 � 136 0 41.8 Ge 17 � 177 0 8.3 17 � 178 62.81 3.0 IKS-25 209 48.75 3.0 20

10 �269.8 3.0 Ge 2211 �58.88 40.6 2212 35.24 3.0 Ge 2013 69.18 4.0 2014 �35.24 3.0 ZnSe 1815 �48.75 18

Table 3. Optical Characteristics of the IR System

Equivalent focal length (mm) �73Focal length of the frontal meniscus (mm) 48.9Focal length of the lens (mm) 78Entrance pupil diameter (mm) 36Distance of entrance pupil to first surface (mm) �50Field of view in the line (°) 9Field of view in the frame (°) 6Equivalent F�# 1:2Linear magnification of the image-transfer

optics�0.935

Back focal length (mm) 20.9Wavelength band (�m) 8–12Values of radius R in Table 2

R1–R2 Frontal meniscusR3–R4 Afocal meniscusR1–R4 LensR5 Field stopR6–R7 PrismR8–R11 Collimating componentR12–R15 Focusing componentIKS-25 Infrared glass

n �10.6 �m � 2.7657n �8 �m � 2.7728n �12 �m � 2.7612.

Table 4. Sequence and Numbers of Field Points

ConfigurationNumber

Field Points ofFig. 3

1 1, 2, 32 4, 5, 63 7, 8, 94 10, 11, 125 13, 14, 156 16, 17, 18


nitude and sign for all six configurations. Thereforesubsequent use of the image-transfer optics makes itpossible to correct aberrations within the length ofthe linear detector array to provide good image qual-ity throughout the field of view.

Thus aberrations in the IR zone-scanning systemare corrected in two steps, namely,

1. Compensating for aberrations of a prismthrough aberrations of a lens such that residual ab-errations of a lens–prism system have a constantvalue within the working angle of prism rotation.

2. Compensating for these residual aberrations bymeans of image-transfer optics to obtain an optimumquality image on the detector.

Figure 6 shows an end-to-end calculation of spotdiagrams for all six configurations of a wide field ofview. Calculations were carried out by use of theoptical design program ZEMAX-10 by the multicon-figuration method, i.e., when the values of all param-

eters of Table 5 were introduced into the meritfunction at one time.

The uppermost row indicates the configuration pro-gram number; at the top left a scale rule is provided.The scale is equal to 0.2 mm. For comparison withperfect image quality an Airy disk equal to 0.052 mmis included. As may be seen from Fig. 6, the spreadspot for scanning zones E and J (configurations 1–3)fits into an Airy disk, which is not the case for zonesD and G (configurations 4–6).

If the prism thickness is reduced by 0.2 mm forslope angles of 1°45=, spread spots for zones D and Gtake the acceptable values given in Fig. 7, suggestingthat the aberrations have been reasonably well cor-rected throughout the field of view.

As mentioned above, the lens has one particularfeature to enhance the F�# of the IR system for thefield angles of the field of view. Using ZEMAX soft-ware, we performed a calculation of transmission T%of the prism and the whole IR system for � 10.6 �mcomponents made of germanium and other materials

Fig. 5. Spot diagrams broken down into six configurations in theF1= plane [Fig. 1(a)].

Fig. 6. Spot diagrams in the detector plane for a prism of equalthickness.

Table 5. Parameters Required for Calculation of IR System Image Quality in the Direct Ray Trace

ConfigurationNumber of

Data

Number

1 2 3 4 5 6

d 5 7.1 6.9 6.7 7.0 6.8 6.6d 6 41.8 42.2 42.6 42.0 42.4 42.8d 7 8.7 8.5 8.3 8.6 8.4 8.2� 1 �0.02 �0.02 �0.02 1.4 1.4 1.4� 2 0.7 0.7 0.7 2.15 2.15 2.15� 3 1.45 1.45 1.45 2.95 2.95 2.95tan � J, G 0.03 0.03 0.03 0.0933 0.0933 0.0933tan � J=, G 0.03 0.03 0.03 0.0933 0.0933 0.0933� 1 0 3.25 4.55 0 3.25 4.55� 2 0 3.25 4.55 0 3.25 4.55� 3 0 3.25 4.55 0 3.25 4.55tan � J, G 0 0.1405 0.2 0 0.1405 0.2tan � J=, G= 0 0.1405 0.2 0 0.1405 0.2


that are coated. Calculation results are as follow (seeTable 6): For configurations 1 and 6, transmission T%is 97.4% and 84.6%, respectively; for the IR system,T% is 81.5% and 82.1%. As these values show, whenthe coated facets of a prism are rotated at an angle of11°20� given a slope of 5°25� (configuration 6), trans-mission T% is reduced by 12.8% compared to that inconfiguration 1. At the same time, for the IR systemon the whole, transmission for the sixth configurationis not reduced but does increase by 0.6% the enhanc-ing image contrast at the edges of the field of view.

In closing, it may be said that the frontal meniscusshifts along the optical axis to athermalize displace-ments of the image plane when the IR system isoperated within a temperature range of �50 °C. Theimage quality remains virtually unchanged. In a nor-mal environment this shifting may be used to focusthe IR system on an object distance of up to 10 m.

Table 2 summarizes the design features (radii ofcurvature R1–R4) of the lens. From the equation

f0� � L�a tan � (15)

one can find the focal length of a lens while specifying�0 � 1.5 � 10%, the focal length of the frontal me-niscus, and its radii of curvature R1 and R2 from Eqs.(1) and (2).

At the same time, while the ratio between radii ofcurvature of afocal menisci R3 and R4 has been foundaccording to Eq. (8), the values of these radii them-selves are not known, because thickness d3 of theafocal meniscus is not known.

Experience in calculating such systems indicatesthat the condition R3 � �d6�4 will be a quite goodapproximation for selecting a value of R3. Given thepowerful software available, one could calculate anIR system with good image quality based on thatcondition alone but taking into account recommenda-tions given while Table 2 was being compiled. Thefinal optimization of parameters of an IR system thatuses image-transfer optics should also be made with

a merit function including the data of Table 2. Thedesign of the image-transfer optics may be arbitrary,subject to specification of requirements.

Conditions (8) and (12) may be disturbed to someextent �10–15%� owing to balancing of higher-orderaberrations and other factors, for instance, the needto obtain a big air space d2 or d4.

6. Conclusions

In designing an optical IR zone-scanning system weobtained the following positive results:

1. The lens compensates for prism aberration tothe same level for all points of field of view.

2. The image-transfer optics brings the level ofcorrection of aberration to the diffraction level.

3. The image interval plane is located in front ofthe prism, making it possible to place a field stop in itand reduce the noise background that is due to thepreceding layout elements.

4. A bundle of parallel rays travels between ele-ments of image-transfer optics, making it possible, byshifting the focusing component, to focus the imageon the detector without changing the image scale(superposition or zone skipping).

5. An original lens design caused the Abbe sinecondition to be disturbed, making it possible to en-hance the F�# for the field bundles of rays and tocompensate for losses of illumination when the prismis rotated.

6. The shifting of the frontal meniscus of the lensnot only allows the IR system to be focused on anobject distance without sacrificing image quality butallows thermal drifts of the image plane to be auto-matically compensated for as well.

References1. G. Gaussorgues, La Thermographie Infrarouge. Principes—

Technologie—Applications, Technique et Documentation (Lavoisier,Paris, 1987).

2. P. J. Lindberg, “A prism line-scanner for high-speed thermog-raphy,” Opt. Acta 15, 305–316 (1968).

3. M. Miroshnikov, Theoretical Grounds for Optoelectronic De-vices. Manual for the Institutes of Higher Education (Mashino-stroyenie, Leningrad, 1977), pp. 113–119.

4. N. Kulikovskaya and I. Valiayeva, “Influence of scanning prismon TV-image quality,” Proc. State Opt. Inst. 41(173), 53–56(1976).

5. A. I. Belousov, “IR zone-scanning system,” Russian patent2,244,949 (20 January 2005); Int. Cl. G02B 26�10, H04 N5�33.

6. I. Turygin, Applied optics (Mashinostroyenie, 1966), Part II.7. B. Nefedov, Techniques for Solving Tasks in Computational

Optics (Mashinostroyenie, 1966).

Fig. 7. Spot diagrams in the detector plane for a prism of unequalthickness.

Table 6. Calculation of T% Transmission

Method Configuration T, %

Prism 1 97.46 84.6

IR system 1 81.56 82.1


infrared zone-scanning system

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