Revised: August 1, 1998

July 1, 1994

The Maryland Revolving-Field Monitor: Theory of the Instrument and Processing Its Data

Mark Edwards, Zygmunt Pizlo, Casper J. Erkelens, Han Collewijn, Julie Epelboim, Eileen Kowler,

Michael R. Stepanov, Robert M. Steinman

CENTER FOR AUTOMATION RESEARCH

Laboratory for Basic Research in Sensory Systems

UNIVERSITY OF MARYLAND COLLEGE PARK, MARYLAND

207420441 1

Revised: August 1, 1998

July 1, 1994

The Maryland Revolving-Field Monitor: Theory of the Instrument and Processing Its Data

Mark Edwards1, Zygmunt Pizlo2, Casper J. Erkelens3, Han Collewijn4, Julie Epelboiml, Eileen Kowler5,

Michael R. Stepanovl, Robert M. Steinmanl

'Psychology, University of Maryland, College Park, MD 2Psychological Sciences, Purdue University, West Lafayette, IN

'Biophysics, University of Utrecht, The Netherlands 4Physiology, Erasmus University Rotterdam, The Netherlands

'Psychology, Rutgers University, New Brunswick, NJ

Abstract This report contains a complete description of the method for processing the data from Table Experiments collected by the Maryland Revolving-Field Monitor (RFM). The apparatus used in these experiments included magnetic-field-sensor coils worn on each of the subject's eyes (sensor-coils), two non-coplanar coils attached to the subject's forehead (head-coil device), and a sparker device attached to the subject's head (head-sparker). The raw data recorded from this apparatus included horizontal and vertical eye angles for both eyes, horizontal, vertical, and torsional head angles, and distances from the head sparker to each of four microphones all in real time.

All of the above raw data are processed to produce quantities that can be used to analyze the eye-movement behavior of subjects who participated in the Table Experiments. Such quantities include the real-time lines-of-sight of the subject, horizontal and vertical gaze- errors relative to a given target, table gaze-positions, and target and ocular vergence. All of these analysis quantities can be determined once the real-time positions of the sighting- centers of both eyes are known

The body of this work contains a description of the RFM apparatus, descriptions of various calibration activities performed during the Table Experiments, derivations of the equations relating the subject's real-time sighting-center positions to the raw data colected by the RFM, and derivations of the equations that relate the sighting-center positions to the analysis quantities mentioned above. The report concludes with three appendixes that contain Table Experiment calibration details, introductory material regarding vectors and matrices, and a derivation of the basic equation used to determine the elements of the matrix describing an arbitrary rotation.

Support provided by AFOSR Grants 91-0124, FA9620-92-J0260 and F49620-94-1-0333

Contents

1 Introduction 6

2 The Maryland Revolving-Field Monitor (RFM) 8 2.1 Revolving-Magnetic-Field Monitor System (RMFM) . . . . . . 8 2.2 Sparker Tracking System (STS) . . . . . . . . . . . . . . . . . 13 2.3 RFM Worktable . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 RFM Coordinate Systems . . . . . . . . . . . . . . . . . . . . 14

2.4.1 The Sparker Coordinate System (SCS) . . . . . . . . . 15 2.4.2 The Table Coordinate System (TCS) . . . . . . . . . . 15

2.5 Types of Measurements Collected in the Table Experiment . . 17 2.5.1 Horizont a1 and Vertical Eye- Angles . . . . . . . . . . . 17 2.5.2 Horizontal, Vertical, and Torsional Head-Angles . . . . 19 2.5.3 Sparker Distances . . . . . . . . . . . . . . . . . . . . . 20

3 Table Experiments 25 3.1 Calibration Measurements . . . . . . . . . . . . . . . . . . . . 25

3.1.1 Sparker Calibration . . . . . . . . . . . . . . . . . . . . 26 3.1.2 Eye-Coil and Head-Coil Offset Calibration . . . . . . . 26

4 Calculation of the Subject's Sighting-Center Position in Real- Time 29 4.1 Finding the Sighting-Center Position . . . . . . . . . . . . . . 30

4.1.1 Transformation of the Rigid Body . . . . . . . . . . . . 33 4.2 Calculation of the Sparker Position . . . . . . . . . . . . . . . 40

4.2.1 Finding the SCS Coordinates of the Sparker . . . . . . 40 4.2.2 Transforming From SCS to TCS Coordinates . . . . . . 42

4.3 Calculation of the Rotation Matrix . . . . . . . . . . . . . . . 44 . . . . . . . . . . . . . . . . . . . 4.3.1 Specifying a Rotation 45

4.3.2 Fick and Helmholtz Coordinate Systems . . . . . . . . 46 . . . . 4.3.3 Derivation of the Single-Axis Rotation Matrices 53

5 Summary of the Data Processing Method 73 5.1 Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Outputs 75 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Processing 75

5.3.1 Compute mirror- trial averages and initial head-sparker . . . . . . . . . . . . . . . . . . . . . . . . . position ; 76

5.3.2 Compute the Vector from Head-Sparker to Eye with the Head in the Standard Configuration . . . . . . . . 79

5.3.3 Compute Sighting.centers, Gaze Errors, and Table Gaze Positions at each RFM burst of Trial n . . . . . . . . . 80

6 The Real-Time Line-of-Sight of the Subject 83 . . . . . . . . . . . . . . . . . . 6.1 Definition of the Line-of-sight 83

6.2 Obtaining the TCS coordinates of the Line-of-sight Vector . . 84 . . . . . . . . . . 6.2.1 Derivation of the Line-of-sight Vector 85

6.2.2 The Instantaneous Line-of-sight Velocity Along a Saccade 86

7 Gaze Errors and Table Gaze Positions 89 . . . . . . . . . . . . . . . 7.1 Horizont a1 and Vertical Gaze Errors 90

. . . . . . . . . . . . . . . . . . . . . . . 7.2 Table Gaze Positions 93

8 Target and Ocular Vergence 96 8.1 The Instantaneous Helmholtz Coordinate System of the Subject 96

. . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Target Vergence 99

. . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Ocular Vergence 100 8.3.1 Determining the Helmholtz Angles of the Line-of-sight

. . . . . . . . . . . . . . . . . . . . . . . . unit vector 102 8.3.2 Instantaneous Vertical and Horizontal Ocular Vergence 103

. . . . . . . . . . . . . . . 8.4 The Instantaneous Cyclopean View 103 . . . . . . . 8.4.1 The Instantaneous "Binocular Gaze Point" 104

A Determination of the Sighting-Center with Subject on the Biteboard 111

. . . . . . . . . . A . l Determining the Sighting-Center of the Eye 111 . . . . . . . . . . . A.2 Details of the SCS to TCS Transformation 112

B Vectors and Matrices 115 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.l Vectors 115

. . . . . . . . . . . . . . . . . B.l.l Components of a Vector 116 . . . . . . . . . . . . . . . . . . . . B.1.2 Addition of vectors 116

. . . . . . . . . . . B.1.3 Dot and Cross Products of Vectors 119 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2 Matrices 121

. . . . . . . . . . . . . . . . . . B.2.1 Definition of a Matrix 121 . . . . . . . . . . . . . . . . B.2.2 Operations with Matrices 123

C The Rotation Formula 126 . . . . . . . . . . . . . . . . . . . . . . C.l The Rotation Formula 126

Supplement Table Coordinates from Sparker Data us ing any Three Microphones ................................... 130