JOSA LETTERS

Instrumentation for the Farnsworth-Munsell 100-hue test* Gordon B. Donaldson†

Department of Physics, University of Lancaster, Lancaster, England (Received 28 June 1975)

Standard Farnsworth-Munsell (F-M) disks and caps are numerically encoded in a two-digit, base-five, system using resistors and zener diodes connected to miniature jack plugs. When the subject orders the disks in the usual way, he connects the plugs to sockets that are in turn connected to an electronic processor. The various error scores are computed, and the error-versus-position graph plotted by a pen recorder, in a total time of between 0.5 and 2.5 min.

The 100-hue test introduced by Farnsworth1 has found a wide and continuing use in both clinical and research pract ice . 2 A set of 85 disks, mounted with colored faces showing through holes in black plastic holders ("caps") and numbered on their reverse sides, is d is­tributed between four boxes in groups of 22, 21, 21, and 21, respectively. Disks 0-21 cover a range from pink to yellow, 22-42 yellow to green, 43-63 green to purple, and 64-84 purple back to red. Each group is randomized, and the subject is asked to rearrange it into a smooth color sequence between two reference disks fixed at either end of the relevant box. These reference disks have the correct colors for the end of the previous box and the beginning of the next box, r e ­spectively. Thus box II ends with the reference disk 43. Any arrangement within a box is permissible, but transposition of disks between boxes is not permitted.

The test is scored by noting the numbers (d„) of the disks that are placed at each of the 85 locations n, and calculating e r ro r scores ,

The size of εn is an indication of how well the disk at n is ordered with respect to its immediate neighbors, rather than a measure of how far from its correct lo­cation it has been placed. The minimum value of εn, corresponding to correct order, is 2. Farnsworth1

does not make clear how εn should be calculated when n is the first or last position in a box: Some users em­ploy the fixed disk for calculation purposes, whereas others t reat the 85 movable disks as a single circular ser ies and, ignoring the reference disks, choose for dn+1 or dn-1 those that the subject has placed first or last in neighboring boxes.

A polar graph is prepared on which the values of εn

are plotted radially. Users differ on the choice of azimuthal (θ) coordinate, however, for although F a r n s ­worth1 instructed that εn should be plotted at the θ co­ordinate corresponding to the cap value dn, it is quicker, and does not usually alter the final graph very much, to ascribe the location positions n to the successive values of θ . 3 This latter procedure, of plotting ser ia l ­ly in n, so that εn is plotted at the point where the disk appears, and not where the disk ought to be, is in reg­ular use by several groups.

Subtotal e r ro r scores S=∑box(επ - 2 ) are calculated

for each box, together with a grand total G=∑a l l boxesS. The choice of the θ coordinate does not affect S or G.

Because both plotting and calculating procedures are tedious, it can take longer to score the test than to do it, thus wasting skilled staff time and preventing mass use of the test, despite its basic simplicity. We have therefore made an electronically scored modification that performs these tasks automatically and quickly. We paid special attention to making the new disk and box sets inexpensive and detachable from the main part of the processor, so that several sets can be used in association with one system.

The central problem was to devise an electrical coding arrangement for the numbered disks that was cheap, small enough not to change significantly the size of the basic cap-disk element (~ 1 cm dimensions), and simple enough to handle so that young children could continue to be able to do the test. Our solution (Fig. 1) uses a standard 2-pole miniature jack plug that car r ies a ± 2% metal-film res is tor and a ± 2% zener diode, con­nected in parallel . The res is tor value and zener-diode breakdown voltage are each chosen from one of five standard values which represent the digits 0 to 4. The combination therefore represents a two-digit, base-five code; the res is tor provides the less-significant digit (LSD) and the zener provides the more-significant digit (MSD). This is adequate to code all of the disks in a single box; we repeat the same code in successive boxes: for example disk numbers 17, 38, 59, and 80 all have the base-five code 32.

Standard caps screw on to adaptors attached to the

FIG. 1. Schematic of disk coding elements, jack sockets, and connections to commutator in processor.

248 J. Opt. Soc. Am., Vol. 67, No. 2, February 1977 Copyright © 1977 by the Optical Society of America 248

FIG. 2. Copy of part of typical output graph, with table show­ing the numbers (dn) of disks placed at locations n, together with the derived εn. The off-scale εn are computed by a sub­program.

jack plugs (Fig. 1). The usual boxes carry 21 (or 22) jack sockets, mounted in line; the test subject has s im­ply to lift the cap-jack combination from a holding slot and insert it in the appropriate socket. A separate lead feeds one side of each jack; common return lines connect alternate sockets. These leads are taken di­rectly to a 30-wire connector at the end of the box; there are no other electrical or electronic components within the boxes.

When the subject has dealt with all four boxes, they are connected to the processor, whose first stage is a transistor commutator that connects successive r e s i s -tor-zener combinations to ground through a fixed r e ­sistor R0. Two interrogating voltages are then applied at A. The first (VM) is large enough to turn on any zener diodes in the interrogated circuit, and so gives an output VBM = VM - Vz that is independent of the value of the resis tor R1; the second (VL) is low enough to ensure that any zener diode in the circuit would be nonconduct­ing, and gives VBL = VLRl /(R1+R0), which is indepen­dent of Vz. The MSD and LSD are thus determined by comparing VBm and VBL in turn with s taircases of 5 reference voltages, generated from intermediate r e s i s ­tors and zener diodes, corresponding to digit values ½, 1½, • • • 4½.

A transis tor- t ransis tor logic (TTL) control circuit processes the digitized disk values according to Eq. (1), generating pulse trains that increment display counters and step a digital pen recorder . The latter consists of a turntable that is incremented in steps of 1/85 revolution by a stepping motor, a radial pen drive system also driven by a stepping motor, and a pen-lift mechanism. The processor first checks that all 85 disks are proper­ly seated in the sockets, then ensures that there have been no transpositions between boxes, and finally gen­erates the circular graph (see example in Fig. 2). The

trace is "open jaw" when εn > 16 (off scale), but the dis­play counters still accumulate properly and show the correct grand total G when the plot is complete. Sub­sidiary programs calculate the subtotals S, and also display the values of the various off-scale e r ro r scores . The electronic processing time for the main and secon­dary programs is about 4 s, but this is extended to be ­tween ½ and 2½ min for production of the graphs, be­cause of mechanical inertia in the plotter.

The materials cost was £60 ($120) for a set of boxes and £240 ($480) for the processor and graph plotter.

Our method treats the disks as a single continuous ser ies and ignores the fixed disks. [Arithmetic that could involve disks from two boxes at once would r e ­quire the addition of 21 (or 22) to those in the later box, to compensate for the repetition of the coding scheme.] However, it would be simple to convert to the alterna­tive method of locating the box ends. Likewise, al­though we follow Kinnear3 and plot location, rather than cap number, serially in θ, the system could be changed to follow Farnsworth 's instructions on this point.1 The processing time would be extended by about 10 s, and so would not significantly affect the plotting time.

The system has been in operation for one year, and has been clinically very successful. The choice of two-digit coding on a simple jack plug has proved entirely justified, avoiding as it has on the one hand the cost of the high-precision elements needed for single-digit (analog) coding, and on the other the location complexity inherent in binary coding, for which 5 bits and as many poles would be needed.

The author thanks Dr. W. O. G. Taylor for interest and for clinically testing the equipment, acknowledges technical help from the late Mr. R. P . Dunn, and Mess r s . N. Bewley, D. H. Bidle, and J. M. Watson.

A fuller account of the apparatus is available in microfiche4 (copies available from the author).

*Work supported by Ayrshire and Arran Health Board, W. H. Ross Foundation and James Weir Foundation.

†Present address: Department of Applied Physics, Univer­sity of Strathdyde, Glasgow, Scotland.

1D. Farnsworth, J. Opt. Soc. Am. 33, 568 (1943). 2 See, for example, articles by Lakowski, Taylor, and others

in Proceedings of the 2nd International Symposium on Colour Vision Deficiencies 1973, Mod. Prob. Ophthamol. 13(1974).

3P. R. Kinnear, Vision Res. 10, 423 (1970). 4"See AIP document no. PAPS JOSAA-67-248-32 for 32

pages of description of the apparatus. Order by PAPS number and journal reference from American Institute of Physics, Physics Auxiliary Publication Service, 335 East 45th Street, New York, N.Y. 10017. The price is $1.50 for each microfiche (98 pages), or $5 for photocopies of up to 30 pages with $0.15 for each additional page over 30 pages. Airmail additional. Make checks payable to the American Institute of Physics. This material also appears in Current Physics Microfilm, the monthly microfilm edi­tion of the complete set of journals published by AIP, on the frames immediately following this journal article."

249 J. Opt. Soc. Am., Vol. 67, No. 2, February 1977 JOSA Letters 249