These spherical maps are sometimes referred to as "HRTF datasets".  An HRTF dataset is ultimately as specific and individual to a listener as their fingerprint.  Some listeners can perceive reasonable 3D cues generated from the HRTF's of general, modeled, dummy-head, or other individual's datasets.  But ultimately, there may be hundreds, thousands, even millions of HRTF datasets stored in the world. 

In 1991, Crystal River Engineering, a pioneering company in real-time, interactive, positional 3D audio, coined the term "Acoustic Head Map" (AHM) to refer to a full sphere map of HRTF's for one individual.  A file-format was created after the input of many interested parties.  Ten years later AuSIM extended the AHM format to other filter files related to 3D audio, formalized and published the file format, and began distributing tools to support it. 
 

Binaural HRTF Dataset
Binaural HRTF datasets are the original and most common AHM file type.  Files of this type are flagged with the ".AHM" extension. 

• Linear-Phase
  Early HRTF's were distributed as linear-phase finite impulse response (FIR) filters.  A single HRTF is comprised of two FIR filters for the left and right ears, each contributing the phase, level, and spectral differences for the respective direction. 
• Minimum-Phase
  Minimum-Phase HRTF's extract the phase from the impulse response as a separate delay term.  The delay can be expressed absolute for each sink, or for binaural data, may be expressed as an interaural difference (ITD).  Filter interpolation is much improved with phase-aligned impulses; interpolating the delay separately.  Early linear-phase HRTF's were reported with 20 milliseconds of response.  After removing the directionally-common bass response and extracting delay, miminum-phase HRTF's required less than 3 milliseconds of response.  Critical-band smoothing further reduced the required response to 2 milliseconds. 
• Normalized
  Normalized HRTF's extract the relative level from the filters, and stores them as a separate data element.  Level extraction yields more flexiblity to the dataset in many ways. 
• Non-Regular
  Early HRTF's were measured on a regular bearing grid of azimuths and elevations.  This causes the density of HRTF's to vary across spherical latitude, and inversely to perceptual priority.  Storing each HRTF and its precise bearing allows arbitary spatial sampling.  Triangulation may be either dictated by the AHM, or performed by the renderer. 
• 3D Range
  Common HRTF's assume propagation from the far-field and thus planar waves.  However range matters, and specifying HRTF's by distance and bearing creates 3D data maps. 
• Tracked Measurements
  Some HRTF measurement systems can measure the actual subject attitude at the time of each measurement intended to be "on-grid".  Corrections can be made in the processing before saving the AHM, or the tracked position and attitude errors can be reported in the AHM, allowing the renderer to choose how/if to correct or render the data. 
• Component Filters
  An HRTF dataset represents a set of related filters.  A properly-processed HRTF dataset will have no common component to all filters, as that would be direction-independent coloration.  But given a suitable basis of component filters, any single HRTF filter can be represented as a linear weighted-combination of those components.  Principal Components Analysis is a sound means of constructing a set of basis functions (components), computing the linear weighted combinations to represent each HRTF filter, and order the basis functions by weighted importance.  Since the component filters are not interpolated, they may be represented by efficient infinite impulse response (IIR) filters. 

Multi-sink Transfer Function Datasets
Multi-Sink directional transfer function (DTF) datasets are identical to binaural HRTF datasets, except that the number of channels (sinks) is greater than two.  Multi-sink AHM's support geometry for the loudspeaker positions and attitude and support channel names and mappings.  Files of this type are flagged with the ".AHM" extension. 

• Vectsonic
  AuSIM3D Vectsonic creates a 3D loudspeaker display using multi-sink directional transfer functions.  One method of computation called Vector-Based Amplitude Panning (VBAP) only utilizes levels to weight a signal distribution to each loudspeaker.  The multi-sink AHM supports more advanced methods employing phase and spectral coloration. 

• Binaural Headphone Equalization
  A proper 3D audio presentation will account for headphone coloration to ensure that the signals within the ear canal are correct.  The HRTF filters have been optimized for directional differences and are very short, representing mostly frequencies over 400 Hz.  Headphone correction must compensate for most of the range of the headphone, and are thus much longer filters.  Keeping headphone equalization separate allows the choice of headphones and HRTF subject to be independently selected at run-time.  Further, the un-changing headphone equalization can be represented with an efficient infinite impulse response (IIR) filter. 
• Multi-Sink Phase, Level, Color Compensation
  Loudspeaker array displays require precise tuning for phase, level, and spectral compensation.  The multi-sink EQF makes use of the phase/delay data terms, which were not required in the binaural variant.  Channel names and mappings are also supported. 
• Per Channel Cross-Over Band-Pass Filters
  Loudspeaker and binaural displays can be composed of split frequency ranges.  The EQF can convey digital cross-over information to support satellites, mid-ranges, woofers, sub-woofers, and vibrating plates. 

• Incident Angle of Reflection Absorption Filters
  Typically reflection AFM's are single axis filter arrays.  Reflection AFM's are utilized by OKA material-model plugins for the AuSIM3D rendering engine. 
• Non-Uniform Atmospheric Absorption Filters
  Typically absorption AFM's are multi-axis filter matrices.  Atmospheric AFM's are utilized by OKA propagation-model plugins for the AuSIM3D rendering engine.