1. Conventionally, OFD is defined as the vergence error relative to a monocular reference. In short-term comparisons (interleaved calibrations), the difference between a binocular fixation and a monocular fixation is giving a monocular component of FD. The added components of the left and right eye give the complete OFD.
2. Although such a reference is necessary to quantify the amount and direction of OFD, is is rather a formal, methodological reference, which – as such – might have no physiological meaning or relevance, because the binocular system is not able to use the state of monocular vision as a reference, because in natural conditions vision is continuously binocular. (To this argument, John Semmlow mentioned that diplopia is the stimulus for vergence, although in his models it is FD=stimulus minus response)
3. If a binocular calibration is applied, a OFD may exist during calibration which thus remains undetected: any OFD that is found in the binocular test phase (e.g. during reading in Antje Nuthmann’s study) represents just the difference between the OFD during reading and the OFD during binocular calibration (OFDread – OFDcal), while OFDcal itself remains unknown.
4. Most earlier FD studies used an interleaved presentation of monocular and binocular presentation (referred to as occlusion method by Fogt and Jones). However, this is a rather unnatural viewing condition, so that we are unsure whether the resulting measures of OFD (typically very small in amount) may represent the condition of natural binocular vision. The latter is better represented by the so called direct method (Fogt and Jones) or blockwise presentation where a longer period of binocular vision is used and monocular calibration phases are given before and after. FD may increase and adapt in such longer binocular phases).
5. Some of our experimental observations suggest that the OFD is larger in the direct procedure than in blockwise procedure, particularly with longer periods of time.
6. We have to take into account that the OFD differs between experimental tasks and viewing conditions (even at a fixed viewing distance).
   1. We know that also with a binocular calibration, an OFD can results in the subsequent binocular task; thus, the two binocular conditions (calibration and task) have different OFDs.
   2. The OFD tends to increase in a series of fixations, e. g. in reading.
   3. Mathew showed that OFD increases in series of binocular fixations (point in circle, lines, word) and that the font size of the letter (16 versus 24) had effect on OFD at the point in circle and at the lines (“adaptation” of OFD)
7. All these differences between tasks can be quantified by having referenced the OFD relative to a monocular calibration.
8. However, can we be sure that the monocular fixation with calibration targets is the appropriate reference for all these tasks?
9. One could think of the following possibility: If we run each of the above tasks (with it’s particular spatial and temporal characteristics) monocularly, and take the resulting fixation points as the reference for the binocular run. In this procedure the monocular reference would include the particular spatial and temporal characteristics of the actual task and the resulting OFD represents the difference induced by binocularity. More concrete for reading: in monocular reading, each eye will land at a particular position within the word. (Is it the same with the two eyes ???). The resulting “pseudo FD” is (L–R)mono_word and represents the reference for the binocular status (L-R)bino_word. In this way, the particular spatial and temporal characteristics of the task would be included in the calibration and the binocular run gives only the change in fixation positions induced by the condition of binocularity. This concept may be a solution for the problem and uncertainty that in monocular calibrations we are not at all sure that the subjects fixate the point on the target as we assume. We have no other possibility (if we do not measure the position of the projection on the retina) than to attributed a value of zero the signal resulting when we have instructed to subject to fixate the monocular calibration target (and can only hope and assume that the subject will do). And we conventionally assume that these monocular reference positions apply to different tassk, but we can have no proof that this is really the case. From all these arguments it may be a solution to run the task to be investigated both monocularly and binocularly and to calculate the difference. We may call this the “Task Specific Monocular Calibration” = TaSMoC
10. However, there are some questions concerning the Task Specific Calibration:
    1. Is still is a monocular condition that does not occur in natural vision thus the visual system does not have this information for operating.
    2. The disparity plane corresponding to the task Tasmoc is arbitrarily. We have no evidence that this disparity plane would be physiologically be optimal.
    3. If one could believe that in reading the monocular fixation positions represent an optimal condition, any deviation by binocularity may represent an impairment. One could judge, whether just by binocularity the landing positions are shifted by which extend. However, monocular reading itself may represent a non-natural condition, since typically an advantage is observed in reading (speed, e.g. isn’t it ?)
    4. Is this pseudo vergence different for different tasks? For testing this: calibrate the eye tracker with points and measure the pseudo FD for reading.
11. All monocular calibrations are artificial and non-physiologically since in the visual system the corresponding disparity plane cannot be represented as a condition to be aimed at. There is no reason why the disparity plane corresponding to Mono Cals may be advantageous to be used by the visual system. Still, Mono Cals can be used as a formal reference for OFDs in different task conditions and the differences between these tasks can still be interpreted.
12. If monocular calibrations are inherently questionable for ecological reasons one may consider possible advantages of binocular calibrations. Given that in the evolution of the visual system, reading played no role, but that the short-term fixation of single targets is a natural task, we may take the latter as a reference during calibration to see whether reading induced any particular differences, e.g. problems with the landing position.

1. SFD represents the central point on the experimental horopter, the line in space were targets are projected onto corresponding retinal points in the two retinae. The corresponding points represent the same visual directions. More precisely stated, to one point on the retina of one eye there is an area in the fellow eye so that these points fall are fused (they lie in Panum’s area). Hillis & Banks suggest that the horopter is the plane where sensory binocular function the two eyes is optimal (stereo threshold, depth discrimination, summation).
2. This is an argument, a physiological reason that the horopter disparity plane is advantages for the binocular system to be used for binocular processing. This argument suggests a new (?) understanding of FD. Since the binocular system has no precise information about the viewing distance, there is no possibility for the system to adjust vergence in a way that the corresponding points (the horopter) lies exactly on the target plane in space. Slight vergence errors may occur (as explained by the Patel model).
3. Optimal sensory performance may occur in a depth plane different from the target plane (which has been shown by Kurtev et al: stereo threshold was minimal at disparity planes with some 10 minarc, these amount however more resemble large (objective) than small (subjective) FDs.
4. The reading research was struggeling with the findings that the two eyes fixate different letters (the centre of a word was not projected on corresponding points in the two eyes – or appeared in different visual directions in the two eyes). This interpretation - however – is implicitely expecting that the “operating” disparity plane is the one that is associated with the target plane.
5. If we assume that the binocular stimulus is best analysed in the plane of the horopter, then alignment of the two monocular representation is achieved in the disparity plane associated with the horopter. In this disparity plane, the stimuli on the two retinae is in complete alignment. No problem is to be expected with respect to different landing positions in the two eyes.
6. In other words: Previous interpretations assume that the binocular evaluation of the stimulus occurs in the disparity plane associated with the “zero disparity” plane (defined by the pseudo vergence as calculated from the monocular calibration). In this plane, misalignment occurs in the case of a SFD.
7. However, we have no evidence that the zero disparity plane is really the relevant one.

The OFD is not relevant, since neither the monocular nor the binocular calibration provides physiologically or functionally relevant measures.

The SFD, as the central point of the horopter, indicates the disparity plane in which the two retinal images are aligned in the cortical disparity representation.

In this sense, the SFD (when deviating from zero) is no adverse condition.

Optometric research suggests that a change of SFD in the exo direction by near vision can cause asthenopia. In this condition, the binocular system is operating in different disparity planes in far and near vision. This may be an adverse condition (see also the impairment of the vergence drifts during gaze shifts as described by Zoi` results.

Is the reference of oFD and sFD the same? oFD=0 equivalent with sFD=0?

Definitions: oFD=0 is defined by the monocular eye positions of the right and left eye during calibration, i.e. (L_mono – R_mono) defined as zero, if the screen centre is defined as zero eye position, (L_mono – R_mono) – V₀, with V₀= 2 arctan (pd/2D) if parallel visual axes are defined as zero eye position.

sFD=0 is defined by physically coinciding nonius lines at the viewing distance. Since dichoptic nonius lines indicate corresponding retinal points, sFD=0 means that the fixation point at the viewing distance D lies on the horopter, i.e is projected on corresponding retinal points. In other words, the fixation point is perceived in the same visual direction in each eye. However, we have to consider that the visual direction coding may be modified by capture effects. If a central fusion target is present, have to take into account shifts in retinal correspondence that modify the horopter following Fogt & Jones.)

This above question (oFD=sFD?) can be stated as: Are the monocular projections during calibration equivalent with corresponding retinal points? No, they generally cannot be equivalent since the horopter is subjects to sensory adaptation due to the actual structure of the fusion stimulus (due to fusional mechanisms), while monocular fixations due not include these fusional mechanisms

Aber Vorsicht mit diesem Argument: Wenn sFD=0, dann geht der experimentelle Horpter durch den theoretischen Horopter. Was bedeutet dies?

The concept of the theoretical horopter includes the assumption the centre opf the foveola is directed towards the fixation point and that the visual directions agree with it. How can it be tested experimentally: Finding cases with oFD=sFD Look at forced vergence FD curves(Fogt&Jones) whether oFD=0 when sFD=0 Regression line of oFD versus SFD pases through origin?