contents

(1)Introduction
(2)Difficulty in odor communication
(3)An Odor Communication System
(4)Odor Spaces
(5)The MTM Algorithm
(6)Applications
(7)Conclusion
(8)References

Abstract

In today’s world most of us are imbibed to the computer world. Here mostly it is based on the human senses. Here the importance of smell and its application to the electronic world is emphasized. Its different parts are de-scribed, and ways to realize them are outlined. In this era, fragrances and flavors have an even greater influence as exemplified by their intensive use in the blooming industries of food and beverage, perfumes and cosmetics, detergents, and many more. These many applications require some means of controlling the odor world. A repertoire of methods in fragrance production and synthesis has been developed, aiming at safe, cheap, and reproducible odor fabrication techniques.

Introduction

It is generally accepted that the sensory world of most humans is built up mainly from visual and auditory impressions, and that other senses, such as smell, have smaller impact. Nevertheless, it seems that the sense of smell is often underestimated, and its impact actually may be overwhelming, directly influencing ancient, primitive, brain paths. Interestingly, humanity has already recognized this a long time ago, perhaps subconsciously , with scents already playing a significant role in ancient religious rituals.

Many applications require some means of controlling the odor world. A repertoire of methods in fragrance production and synthesis has been developed, aiming at safe, cheap, and reproducible odor fabrication techniques. Still, hard labor is required for each individual odor fabrication process, involving tedious, expensive, time consuming research. In the last few decades, there have been efforts to integrate odors into the rapidly evolving world of modern communication. Adding smells to a personal computer, a video, a television set, or a mobile phone, would give rise to a vast number of possible applications, in the fields of commerce, marketing, computer games, and many others. However, available odor technologies seem to be incapable of supporting such applications, making it necessary to develop novel technologies. Today, only simple odor manipulations can be carried out. For example, scented cards are often inserted as sales promoters in magazines, dispensing a fragrance when scratched. Similar “scratch and sniff" devices sometimes accompany movies or home television. Some recent model of mobile phones contains small capsules, emitting pre-determined scents when certain people call. There have even been attempts to introduce odors by means of air conditioning systems in movie theaters and in the workplace. Still, none of the above comes close to the technological advances in vision and audition. One of the most salient expressions of this gap is in modern multimedia. Pictures and sound are routinely transmitted and exhibited on television, video or the personal computer. This has not happened yet with odors.

Difficulty in odor communication

Some of the major problems seem to be the following:

The underlying physics is complex. Vision and audition also involve complex physical phenomena, but photons and sound waves are well-defined physical objects that follow well-known equations of a simple basic nature. Specifically, in both cases sensory quality is related to well known physics. On the other hand, the smell of an odorant is determined by the complex, and only partially understood, interactions between the ligand molecule and the olfactory receptor molecule.

The biological detection system is high-dimensional. The nose contains hundreds of different types of olfactory receptors, each of them interacting in different ways with different kinds of odorants. Thus, the dimensionality of the sense of smell is at least two orders of magnitude larger than that of vision, which can make do with only three types of color receptors.

Odor delivery technology is immature. While artificial generation of desired visual and auditory stimuli is done in high speed and with high quality, smells cannot be easily reproduced. Now-a-days, the best that can be done is to interactively release extracts that were prepared in advance.

Much effort has been invested in trying to better understand the sense of smell and its means of expression. Relating the smell of a molecule to its three-dimensional structure, as well as characterizing ligand-receptor interactions are the subject of intensive research. However, while much progress is constantly reported, no theory adequately dealing with olfaction is currently at hand.

An Odor Communication System

The most general building blocks of such an odor communication system are as depicted in Figure 1. At a remote location (Figure 1a) an input device the sniffer is used to take in the odor and transform it into a digital fingerprint. At a different location (Figure 1b), the fingerprint will be analyzed by the mix-to-mimic (MTM) algorithm, which will instruct an output device. The whiffer to emit a mixture of odorants that will mimic the input odor well enough to fool a human into thinking that he/she actually smells it. Prior to all of this there is also a considerable amount of preprocessing and preparation. All of this will be discussed later on.

This setup is in direct analogy with other communication systems. For example, if we replace the sniffer by a camera, and the whiffer by a printer, we get a visual communication system, with the various color coding (RGB, CMYK, etc.) being analogous to our mixing technique.

The sniffer

In the most general sense, a sniffer is a physical device that can record, or digitize, odorants. In other words, it takes chemical data and turns it into numbers. Upon the introduction of an odorant in its inlet, the sniffer produces a numerical output, which becomes (usually after some further manipulation) a representation, or a fingerprint, of the odorant. To be useful in our odor communication system, we shall further require from a sniffer to be sufficiently discriminatory, in that it produces unique fingerprints for all odorants. Moreover, we would like its fingerprints to exhibit some correlations with the smell perception of their sources. Any instrument that quantifies a certain property of chemicals in a unique and reproducible way suffices. In principle, an apparatus capable of measuring the boiling point of an odorant could become a sniffer. However, we can expect the correlation of boiling points with odor perception to be rather difficult.


A more realistic example is the combination of a gas chromatograph (GC) and a mass spectrometer (MS). The GC/MS combination is very popular in analytical chemistry, and is used to precisely identify the compounds of a mixture. However, we doubt that it would make a good sniffer, since we have no reason to believe that the output it produces has anything to do with smell perception. From a commercial point of view, GC/MS suffers from additional disadvantages: it is expensive, it is large and bulky, and it is complicated to use, requiring carefully-trained operators. Moreover, analyzing its results is time consuming, and often sample preparation is tedious too. In our opinion, the best candidates to serve as sniffers are the instruments collectively grouped under the term electronic noses (e Noses). These are analytic devices, whose main component is an array of non-specific chemical sensors, i.e., sensors that interact with a broad range of chemicals with varying strengths. Consequently, an incoming analyte stimulates many of the sensors in the array, and elicits a characteristic response pattern. These patterns are then further analyzed for the benefit of the specific application. The fact that the biological smelling system also relies on an array of non-specific receptors, gives hope that we may be able to find significant relationships between the biological nose and its artificial counterpart. The usual chemical sensors are replaced by biosensors that are supposed to work in essentially the same way as the biological receptors in the nose. From a commercial point of view, e Noses enjoy several desired properties: they can be made small and cheap; they are easy to use, fast to operate, and for most applications they do not require any special sample preparation.

In the electronic realm, as in the biological one, the desire for sensitivity does not always go well with the desire for non-specificity. Sensors (or receptors) that are designed to respond to an assortment of stimuli are normally characterized by low sensitivity. Indeed, e Noses are typified by relatively high detection thresholds, on the order of 1-10ppm. Although seemingly problematic, this is not a true stumbling block for an odor communication system. First, many odor sources release higher concentrations than this in their immediate vicinity. Second, a preliminary step of concentration enrichment can be always carried out if necessary.

The whiffer

The whiffer is the part of the system that emits the smell imitation to the surroundings. It must include a palette of reservoirs containing the odorants it can mix, a technology to accurately mix them, and means for releasing them to the outside world in accurate quantities and with precise timing. For use by mass consumers, the sniffer should also have small physical dimensions and be of low cost. This definition of a whiffer strongly relies on the assumption that mixtures from within a set of odorants can mimic, to a reasonable level, any desired smell. This is reminiscent of the characteristics of RGB color mixing in vision.

The requirements from a whiffer seem simple, but it turns out that numerous technological barriers must be overcome in order to satisfy them. In fact, whiffers, as we have defined them, are not commercially available. The devices that are closest to being whiffers are the olfactometers, which have been in use for many years and are capable of accurately mixing gas samples and releasing the mixture to the surroundings. They are most often used together with human panelists for the purpose of assessing odor emission levels. However, an olfactometer is not a true whiffer, since it is designed mainly for diluting carefully prepared gaseous samples. We think of a whiffer as being more akin to a printer (say, an ink-jet), with the palette of odorants being analogous to the color cartridge.

The mix-to-mimic (MTM) algorithm

The heart of the system, however, is in its mathematical and algorithmic parts. The ultimate role of these is to instruct the whiffer, based on the input odor detected by the sniffer, as to how to mix the palette odorants so as to produce the desired odor perception.

Odor Spaces

For a proper formulation of the mixing algorithm and the algorithmic processes around it, it is important to introduce the notion of odor space. Our brain carries out a similar operation when we sniff, producing a measurable electrical neuronal activity pattern. We use the term odor space for any end product of a process that represents numerically the olfactory information stored in odor ligands. Specifically, there are three kinds of odor spaces-the sniffer space, the sensory space, and the psychophysical space.

To start with, we use (o; c) to describe an odorant o in concentration c. An odor space represents (o; c) by the set of numbers d(o; c), which we call the odorant vector; the length of this vector is the dimension of the odor space.

The sensory space

The sense of smell is a primeval sense, originating in early single-cell organisms. In principle, it functions by taking a sample of the ambient environment and analyzing its chemical contents. In air-breathing organisms, volatile odorant enter the nasal cavity, where the primary organ of smell, the olfactory epithelium, resides. This pseudostratified neuroepithelium contains 10-100 million bipolar sensory neurons, each having a few dozen mucus-bathed hair-like cellular extensions known as olfactory cilia. The ciliary membranes harbor the olfactory receptor (OR) proteins , as well as components responsible for the chemoelectric transduction process. ORs have all been identified as belonging to the 7-transmembrane superfamily of G-protein coupled receptors. The stereospecific binding of odorant molecules to the ORs initiates a cascade of biochemical events that result in action potentials that reach higher brain centers. The number of distinct types of ORs, r, called the olfactory repertoire size, is believed to be around 1000 in all mammals .Only recently, the full sequence of more than 900 human OR genes has been reported, based on genomic databases . Only about 300 of them are functional in humans, and the rest are pseudogenes. However, in other mammals

the pseudogene fraction could be much smaller. The recognition of odorant molecules occurs in the brain by a non-covalent binding process akin to that encountered in many other receptor types, including hormone and neurotransmitter receptors. However, while for “standard" receptors there is usually only one, or very few, natural ligands, olfactory receptors are functionally promiscuous. Therefore, when an odorant (o; c) approaches the epithelium, it interacts with many receptor types, and can be characterized by the vector




with Ri(o; c) being the response of the i'th type of receptor molecule to the odorant (o; c).We deliberately do not specify the details of the response, which can be the fraction of bound receptors, the concentration of some second messenger, or some other relevant entity. It is often, in fact, a dynamic function of time. We shall see later that the exact definition of Ri(o; c) is irrelevant to our algorithm. The r-dimensional odorant vector dB(o; c) describes the way by which the biological sensory machinery responds to the odorant, so that terming this odor space the sensory space is appropriate. An important observation is that all the 105 to 106 OR molecules in the same sensory cell are of the same type, and thus r is also the number of distinct types of olfactory sensory neurons.

The olfactory neurons send their axons to the olfactory bulb (OB), passing in bundles through the cribriform plate. Here, the first, and rather significant stage of the higher processing takes place. It is widely believed that important aspects of odor quality and strength (concentration) perception are carried out in the OB, and studies have in fact shown that the OB responds with odor-specific spatio-temporal patterns. Successive stimulations with the same odorant have been shown to lead to reproducible patterns of activity. Patterns evoked by low concentrations were

topologically nearly identical to those evoked by high concentrations, but with reduced signal amplitude. Within the OB, the OR axons form contacts with secondary neurons inside ellipsoidal synaptic conglomerates, called glomeruli. A glomerulus serves as a synaptic target for neurons expressing only a single OR type. Consequently, it is not surprising that the number of glomeruli, estimated to be between 1000 and 2000, is of the same order of magnitude as r. From our point of view, the important conclusion is that the OB is stimulated by approximately r distinct types of nerve cells, which tells us that the entire olfactory pathway is triggered by the vector dB(o; c).

The psychophysical space

Upon sniffing, three major tasks are performed by the brain: a qualitative classiffication of the incoming odorant, a quantitative estimation of its strength, and a hedonic decision about its acceptability. The first two are objective tasks (measuring molecule types and concentrations), while the last one is more subjective and will not be dealt with here.

Olfactory classification of a pure chemical or a mixture is a rather elaborate task. Unlike vision, audition and even gustation, olfaction is multidimensional, and is believed to involve dozens, if not hundreds of quality descriptors. Quantitative assessment of these qualities poses real challenges to research in olfactory psychophysics. Methods have been developed to assign descriptors to an odor, and to give relative weights of dominance to the different descriptors. The entire procedure is normally carried out by a human panel of experts who are familiar with the technique, and who are capable of distinguishing the different descriptors with a high degree of accuracy. As appealing as this might sound, it is quite difficult to obtain coherent results with profiling, since exact verbal descriptions of odor perception are too demanding. Human subjects often find it difficult to describe odor quality verbally, an observation supported by the fact that most natural languages have a poor vocabulary for odors, and these are sometimes described using words borrowed from other sensory modalities(e.g., cool, green).

Alternatives to the profiling technique use panels to accomplish simpler, thus perhaps more reliable, tasks, such as various ways of sorting a group of odors, comparing pairs or triples of odors, pointing out exceptions within groups of odors, etc. Some techniques collect enough statistics from the panels to be able to create a distance matrix that quantitatively expresses the level of dissimilarity between pairs of odors. Various kinds of multidimensional scaling (MDS) algorithms can then be applied to the data, resulting in a vector representation of the odors.

Whatever quantitative quality assessment technique is used, an odorant (o; c) is eventually represented by the odorant vector dP (o; c). We use the symbol l to denote the dimensionality of the resulting odor space, which we call the psychophysical space. If one uses odor profiling, then l is normally in the range 20-200, and the i'th element of dP (o; c) is the human panel's opinion regarding the weight of the i'th descriptor. If one uses MDS, l is typically much lower (< 10), and the elements of dP (o; c) do not have precisely describable meaning. We should emphasize that dP (o; c) is concentration dependent, since the perception of an odorant might change with concentration.

We might say that while (o; c) represents the chemical o in concentration c, the odorant vector dP (o; c) represents the human perception of this odorant, or simply its odor. From this perspective, the psychophysical space is the one on which we should focus, since the odor communication system is designed to directly work within it.

There are profound inter-relations between the psychophysical space and the sensory space. The brain itself is the tool that maps the r-dimensional odorant vectors dB (o; c) into their corresponding l-dimensional odorant vectors d P (o; c). Ignoring dynamical phenomena, such as adaptation, this mapping is considered robust, in the sense that identical inputs dB (o; c), evoke approximately the same outputs d P (o; c). This suggests a way to “fool" the human brain: if a certain odorant with a smell d P(o; c) elicits a neuronal response dB (o; c), then the same smell would be perceived if we succeed in developing a mixture of palette odorants that elicits the same neuronal response. The problem is that gathering data on the

behavior of the olfactory neurons is hard, and not much information is currently available. Moreover, the effect of mixtures on neuronal response has not yet been completely unravelled, making the prediction of the effect of mixture perception impossible. For this reason we would like to avoid the necessity of working with the odorant vectors dB (o; c), which leads to working with sniffers and human panels, as we shall see.

The sniffer space

The sensors inside an e-Nose are made using diverse technologies. Depending on the type of sensor, a certain physical property is changed as a result of exposure to a gaseous chemical. During the measurement process a signal is obtained by constantly recording the value of the physical property. Since a typical signal is comprised of a few hundred measured values, a process of feature extraction is frequently required, which is the process of finding a small set of parameters that somehow represent the entire signal.

The set of features extracted from all the signals in a single measurement is called the feature vector, and if there are m features the vector can be viewed as an odorant vector in the m-dimensional sniffer space. When exposed to mixtures of chemicals, e-Noses produce a feature vector that reflects the combined effect of the mixture constituents. Yet, the feature vectors of a mixture do not noticeably differ in any aspect from those of pure chemicals, and in this sense e-Noses do not distinguish pure chemicals from mixtures.

As the brain maps the sensory space into the psychophysical space, we can think of an analog algorithm that maps odorant vectors in the sniffer space to their corresponding odorant vectors in the psychophysical space. We shall call this the mapping algorithm, and denote it by the function f; hence, d P (o; c) =f (d S (o; c)).

The MTM Algorithm

Now that we are equipped with notions of odor space, we can redefine the algorithmic scheme in more accurate terms. Let the whiffer contain n palette odorants, and let ti stand for the i'th of these. We use the generic term to denote an odorant vector that constitutes a representation of palette odorant i in concentration vi in some odor space E. For example, if E is the sniffer space S, then would be the m dimensional odorant vector . If E is the psychophysical space P, then pPi .vi would be l-dimensional odorant vector d P (ti; vi). In this way, p Ei can be viewed as an operator that is applied to the concentration vi to yield some representation of the i'th palette odorant in concentration vi. Notice that we use the symbol vi, rather than c, to denote the concentration of the i'th palette odorant; this is to distinguish the palette odorants from other odorants, for which we use c. We define the mixing vector v = (v1……. vn) T to be the list of palette odorant concentrations in a particular mixture. In accordance with our earlier notations, we represent a palette mixture in the odor space E by PE .v, with v being the mixing vector and PE being an as-of-yet unspecified operator.

Let (o; c) be an arbitrary odorant. The role of the mixing algorithm is to find a mixing vector v, such that the perception of PE _v is as similar as possible to that of (o; c). More formally, we would like d P (o; c) to be as close as possible to PP .v; i.e., we are seeking

with ||.|| some appropriately chosen norm. The general scheme of the mixing algorithm discussed above is described in Figure 2. The sniffer provides the algorithm with a measured odorant vector d S (o; c). The mapping algorithm then transforms this vector into the odorant vector d P (o; c) in the psychophysical space. Following this, based on the specific palette that resides in the whiffer, the algorithm calculates from (1) the mixing vector v, and transmits it to the whiffer. The whiffer then prepares the corresponding mixture and releases it.

We are now in a position to describe our algorithm. In the interest of clarifying its dynamics, we have chosen to describe its development in three stages, each adding a further complication.

Fooling the sniffer

Let us consider first the problem of “fooling" the sniffer. We want to find a way of presenting an e-Nose S with a palette mixture that mimics the original odor it was given. Formally, let (o; c) be an odorant, represented by the m-dimensional odorant vector d S(o; c). We want to find a mixing vector v such that when given PS _ v the sniffer S will produce a fingerprint as similar as possible to the one elicited by (o; c) itself. This is a simplified version of the mixing problem. First, it does not require any space-to-space mapping, since we are working in a single space, the sniffer space. Second, fooling an eNose, whose fingerprints are relatively controllable and are easily measured and studied, seems on the face of it to be simpler than fooling the human perception. Dealing this problem first will provides us with insight regarding the solution of the more general problem.



In analogy with (1), our task is to find a vector v that satisfies

Notice that unlike (1), here the odorant vectors are taken to be in the sniffer space too.
Let us now discuss such a PS in a relatively simple special case. An m-dimensional sniffer space for a sniffer S is called linear if it has the following properties:
(1) Linearity of response: For an odorant (o; c), each of the elements
is proportional to the odorant's concentration. That is,
where is an odorant-dependent constant. Denoting we can write this property in the compact form


(2) Additivity of mixtures: The odorant vector describing the mixture
is the vector sum of the odorant vectors of the individual elements,



For a linear sniffer, the operators pSi are simply multiplications by constant vectors,
Similarly, the operator PS is just a multiplication
by a matrix, If we take ||.||to be the standard
Euclidean norm, then finding v is equivalent to solving the well-known least squares problem,

Actually, v is constrained to be a non-negative vector.
Thus, had the sniffer space been linear, the mixing vector would have been easily calculated as the minimizer of a constrained least squares problem.

Fooling a different sniffer

Suppose now that we have two different sniffer spaces, S1 and S2, with odorant vectors dS1(o; c) and dS2(o; c) of dimensions m1 and m2, respectively. Can we digitize an odorant (o; c) in the first sniffer and then produce a mixture of palette odorants such that the second sniffer will be fooled into thinking it to be (o; c)? No such mapping has ever been proposed. For example, the data provided by a single QMB sensor will probably not suffice to predict the response of some MOX sensor. Single sensor eNoses are, however, not realistic. We claim that for reasonable sniffers, with an adequate multitude of sensors, a good mapping can indeed be found. When a sniffer consists of an array of diverse sensors, it is likely to capture the physical information it needs for characterizing a certain odorant. At least in theory, this information is all that is needed in order to predict the response of another sniffer with similar information content. Put differently, finding the mapping g : S1 -> S2 is more likely to be possible when m1 is large, and when the sensors are as diverse as possible. In our ongoing research, S1 is the MosesII eNose, with its 16 different sensors made up of two completely different technologies.

Once this mapping is found, we would read in the input odor in S1, yielding the m1-dimensional odorant vector dS1(o; c), and then compute the mapping into the space S2, yielding the m2-dimensional odorant vector dS2(o; c). This vector would then be used, to fool the second sniffer, S2.using, our experiments show that the space is adequately linear.

Fooling the human brain

The human nose, with its hundreds of receptor types and complex biological machinery, can be viewed simply as a special case of a sniffer. Like any other sniffer, it takes an odorant (o; c) and represents it by an odorant vector d P (o; c).



However, mapping vectors from an artificial sniffer into the biological human “sniffer" will probably be far more challenging than mapping one e Nose into another. The difficulty is in the fact that the two systems, the biological and the artificial, are very different in the detection mechanism. The olfactory receptors (ORs) operate on very different principles than chemical sensors. As mentioned earlier biosensors for eNoses are being developed by several research groups. Once they are eventually incorporated in e Noses, this difficulty can be expected to be removed. Our point here is that even for “standard" e Noses that use conventional chemical sensors, there is evidence that the resulting fingerprints can be used to infer psychophysical data.

Over a wide range of concentrations between the threshold value and the saturation value, the intensity usually obeys a power law I (o; c) = kcn, with k and n being odor-specific constants. This is definitely not linear, but it has also been observed that n is usually close enough to 1 to allow for the linear approximationto hold in a reasonable range of low concentrations. As explained earlier, real world applications require only low concentrations, thus this linear approximation might very well be adequate for the kind of odor communication system we propose.

Palette odorants

Our odor communication system is based on the belief that there exists a set of palette odorants that can be mixed so as to mimic (up to a certain tolerance) any desired odor perception. Since to the best of our knowledge such an odorant palette has never been realized, the belief in its existence requires some justification. We start with a somewhat philosophical argument, and then provide some experimental observations to support it.

Relevant research indicates that we may assume that if two different stimuli elicit identical response of the ORs, the human perception thereof will be identical. Thus, it is the response of the receptors that has to be mimicked. An

incoming stimulus elicits a spatio-temporal response of the olfactory nerve cells in the epithelium. This response is the combined result of many factors (such as the type of the odorant, its concentration, and its temporal behavior), and it reflects the entire available information regarding the specific stimulus. This information is encoded into the odorant vector dB, which is considered to be the input for the cerebral analysis process. Since this process ends up with the ability to classify the odorant, to estimate its concentration, and to describe it, all this information must be somehow included in the response pattern, yielding the conclusion that identical response patterns will result in the same sensation regardless of the way they were formed. It is now reasonable to assume that any such set of responses can be viewed as a (possibly nonlinear) superposition of patterns, which, when deciphered, can be reformulated as mixtures of suitably chosen palette odorants. Thus, if we can prepare a mixture of palette odorants, whose collective effect on the olfactory nerve cells is similar to the effect of the original odorant, the perception of the mixture will very closely resemble the perception of that odorant.
The fundamental experimental observation that should be considered here is the fact that a mixture is usually perceived by humans as a new odor. This is actually experienced by every individual on a daily basis, with the distinct aroma of food products, beverages, coffee, perfumes, etc., all being odorant mixtures comprising usually hundreds of different odorous volatile chemicals.

Furthermore, the number of glomeruli activated when sniffng a mixture is similar to that activated when sniffng pure chemicals. Similarly, the number of odor qualities perceived by a human panel responding to a mixture is similar to that perceived when responding to pure chemicals. A typical smell is adequately described by 100 unique compounds on the average, then it would drive the number of palette odorants to be impractically large. Fortunately, this is not the case. It is known that even the most complex odors can be mimicked by mixtures of a relatively small number of ingredients. This is nicely seen in the food industry, where people are interested in generating certain smell perceptions using simple artificial blends, known as aroma models. Very complex aromas, such as those in wines, coffee brews, tomato paste, boiled beef and the like, are made of mixtures of many hundreds of chemicals. Yet, certain techniques have been designed to extract

those compounds that have the strongest impact on the smell, and only those are used in the aroma models. Typically, the original smell is reproduced with 10-30compounds at most.

Summary of the MTM algorithm

Devising:
(1)Prepare a (preferably large) database of odorants, and pass them through an appropriate human panel, obtaining the odorant vectors dP (o; c) in the psychophysical space.
(2)Measure the same odorants by a sniffer S, obtaining the odorant vectors dS(o; c).
(3)Learn the mapping f between the sniffer space and the psychophysical space.
(4)Choose a whiffer palette of size n.
(5)Compute the operator PP for the palette odorants. (This is best done by measuring the palette odors directly by the human panel; alternatively, they can be measured by the sniffer S and then subjected to the mapping f.)


Using:

(1) Sample an input odorant (o; c) using the sniffer S, thus obtaining dS(o; c).
(2) Map the resulting fingerprint from the sniffer space to the psychophysical space, dP (o; c) = f(dS(o; c)).
(3) Find the non-negative mixing vector v as the minimizer of

(4) Prepare and release a mixture of the palette odorants according to the vector v.

Choosing the hardware

The algorithmic scheme outlined above can work with any sniffer and any whiffer. Even an extremely poor sniffer, that yields very little information, and a primitive whiffer with a small number of palette odorants and a coarse mixing ability, can be used; the MTM algorithm will produce results and the whiffer will emit the computed mixture -the best possible under the circumstances.

The point is that the results will be only as good as the hardware, and vice versa: better hardware will cause our scheme to produce better results. The situation regarding sniffers is good. More and more eNose types are developed, using continuously improving sensor technologies. We hope that the ideas presented in this paper will have a productive effect on eNose manufacturers, since we envision a far broader spectrum of applications there of.

Whiffers seem to evolve much more slowly. But, as we have shown in our design and construction of iSmell r, the technology is available and the job can be done. We are confident that building and marketing high-quality commercial whiffng devices is possible. Indeed, it is inevitable.

Choosing the palette

One major aspect of the whiffer can benefit from the ideas presented here -the construction of the palette. The two key features of the palette are its size n and the particular palette odorants it contains. A palette designer should be concerned with determining both of these.

In a typical application of our scheme, we expect n to be given, being constrained by the limitations of the technology used, by the desired accuracy and by cost. Let us use the term tolerance, denoted to represent a measure of the extent to which the perception of the computed mixture P P .v deviates from that of the original odorant, dP (o; c). The exact formulation of the tolerance depends on the specific structure of the odor spaces involved.

In principle, a larger palette allows for a smaller tolerance. However, large palettes are more expensive and more difficult to build, hence a compromise between palette size and tolerance must be made. If there were no constraints on the palette, we could simply choose n to be large enough for the palette to contain all possible distinct aromas, which is at least in the order of 104, and very far from the ability of current whiffer technology. To be realistic, we must assume that for the near future n will be under 300.

As to choosing the palette odorants themselves, we envision an algorithm which, given the desired size n and a large collection of candidate odorants, computes the “best" n odorants for the palette. Such an algorithm can indeed be constructed, based on ideas similar to the ones reported upon here, and taking into account accumulated information about the psychophysical space (such as the density distribution of the various odorants). It is not out of the question that such an algorithm could also be used to tailor special palettes to specific application areas, to desired tolerance, to constraints on mixing ratios or quantities, etc.

Another interesting option in palette design is to adopt a multi-tier approach. There might be advantages in building the palette so that the palette odorants are arranged in tiers. In this way, mixtures can be prepared by taking larger quantities from the higher levels (catering for coarser descriptions), adding lower level odorants to fine-tune the output -as a kind of “salt-and-pepper" stage. Of course, the physical reservoirs for the palette odorants inside the whiffer can then be of different sizes, reflecting the differences in the typical use-rates of the various levels.