The quality of positional agreement between pairs of ridge paths in two impressions should not only consider friction ridge skin elasticity stretch and compression thresholds, but also rotational thresholds.  In order to define friction ridge skin elasticity rotational thresholds, the displacement between "ridge vector azimuth angles" between pairs of corresponding ridge formations in two impressions from the same source were examined. 

A ridge vector may be defined as the magnitude (quantitative weight) of a ridge formation that bears direction or aim to its nearest neighbor or “target” minutia (M).  Displaced minutiae targets between ridge vectors from the same source can be measured in terms of degrees using a protractor.  Displacement is a vector quantity, which refers to how far out of place an object is.  It is the object's overall change in position.  The ridge vector may be placed on a circular coordinate system or polar x-y axis in which it’s origin, O, is defined by the point perpendicular and parallel to its adjacent ridges.  The ridge vector’s direction leads from this point, indicated by the arrow (see diagram) and aims at the target neighbor.  In this circular coordinate system, the target neighbor is represented by the spatial distance “r” from the origin and the azimuth angle (θ) between the x-axis and the line from the origin to the target neighbor (minutiae “M”).  (Figure 4 and 5).

 Figure 5

The following frequency of occurrence studies were performed to define tolerance thresholds for precise and relative rotational agreement between ridge vector azimuth angles (θ) between corresponding ridge vectors in known impressions made by the same individual:

Frequency Study #1

A total of 2057 pairs of corresponding ending/bifurcating ridge formations from 39 randomly selected pairs of photographically enlarged rolled vs. flat fingerprint impressions from ten-print cards were used.  Ridge vector azimuth angles for each pair of corresponding ridge formations to its nearest neighbor were measured using a protractor to the nearest 10 degrees.  All of the pairs of azimuth angles, except one, were displaced by less than 10 degrees.  Only 1 pair displayed ridge direction in gross disagreement in which the azimuth angles (θ) for the 2 ridge vectors were displaced by 51 degrees.   This pair of dissimilar corresponding ridge formations was deemed an anomaly and not consistent with normal friction ridge skin elasticity thresholds.
 

Frequency Study #2

A second frequency of occurrence study was performed using 267 pairs of corresponding ending/bifurcating ridge formations from pairs of latent vs. flat fingerprint impressions. The substrate used was 81% glass, 9% metal and 9% plastic.   Each substrate was flat, dry, and relatively clean.  Latent impressions were deposited in a natural, spontaneous manner consistent with normal handling, developed using standard black fingerprint powder, lifted using standard lifting tape, and placed on standard latent lift cards.  The corresponding ridge formations in the latent impressions were then compared to those in the flat impressions from the same source.  Each pair of corresponding ridge vector azimuth angles was measured for positional displacement using a protractor.  As a result, no pairs of corresponding ending/bifurcating ridge vector azimuth angles displayed displacement greater than 10 degrees.   

Based on these two frequency studies, azimuth angle displacement of 10 degrees served as the threshold for relative rotational agreement between ridge vectors.  As a result, "relative" agreement of rotational positions between pairs of corresponding ridge vectors and its nearest neighbors was defined as ±10 degrees.

For purposes of consistency, precise rotational ridge path position agreement between pairs of corresponding ridge vector azimuth angles in two impressions and its nearest neighbors was set to coincide with a similar ratio established between relative and precise friction ridge skin stretch/compression thresholds.  As a result, "precise" agreement for rotational positions between pairs of corresponding ridge vectors and its nearest neighbors was defined as ±5 degrees.

Pairs of ridge vectors with azimuth angle displacement greater than ±10 degrees and deemed within tolerance not to be considered a non-corresponding ridge event were made neutral and not included in the aggregate.  Ridge vectors with multiple nearest neighbors (each target approximately the same distance from the vector) defaulted to the ridge vector displaying the azimuth angle with greatest displacement. 

Ridge path positions were deemed to precisely agree only if both friction ridge skin elasticity stretch/compression and rotational thresholds were simultaneously satisfied.  If either stretch/compression or rotational threshold was deemed relative then the positional agreement for that pair of ridge paths was defined as relative and subject to reduction. 

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During experimentation to observe the effects of fingerprint deposition pressure combined with rotational twisting, Alice Maceo reported a maximum 30-35 degree rotational movement from the core before slippage occurred [97].  Macae video-recorded deliberate fingerprint rotational movement under heavy deposition pressure and recorded these results. 

The same experiment utilizing a larger fingerprint sample from different individuals can be performed to test [and possibly refine] the above thresholds for azimuth angle displacement between pairs of "matching" ridge features in two impressions.  The results for these planned experiments will be published on this page upon completion. 

For purposes of routine casework and based on familiarity with measured stretch/compression and rotational angular displacements, professional judgment may be applied to determine preliminary estimates for precise or relative positional agreement between pairs of corresponding ridge formations in two impressions.  Only when spatial relationships are ambiguous should photographic enlargements be made and distances and/or azimuth angles precisely measured using a ruler and/or protractor.  In any case, the placement of the polar x-y axis, ridge vector origin (O), its aim or direction to its nearest neighbor target minutia (M), and azimuth angle (θ) displacement, should speak for itself and allow demonstration, even to the layman.