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Introduction

The exposure reciprocity law has been proposed based on the concept that a given property is directly dependent on its exposure dose, the product of the irradiation intensity and exposure time, but independent of the individual values of the irradiation intensity and exposure time. This concept for photochemical reactions was first introduced by Bunsen and Roscoe in 1923 and came to be known as the reciprocity law due to work in photography where the blackening of photographic film is indeed dependent only on the exposure dose . The reciprocity law has been proposed or applied to many different fields since that time, including photopolymerization reactions, photoconductance, medicine, and photodegradation, essentially any field where incident radiation is used to generate a response . At its heart, the reciprocity law assumes that the rate of the overall photochemically initiated process is proportional to the light intensity such that the overall amount of the process that occurs will depend only on the dose. While this is true for most primary photochemical processes (e.g., absorption) at reasonable light intensities, secondary processes do not generally observe this relationship.

In clinical dental settings, which makes extensive use of photopolymerization for a variety of applications, curing light types and intensities can vary significantly and differences are especially pronounced as newer lights such as argon ion lasers and LEDs continue to achieve higher irradiation intensities . Common light sources exhibit irradiation intensities ranging from several hundred milliwatts for conventional quartz halogen units up to 2000 mW for modern LED units, and the initiating intensities have been relatively steadily increasing in recent times. It is common in the dental community to approximate curing using these lights based on the reciprocity law, and several studies looking at reciprocity have been performed . Palin and co-workers evaluated the degree of cure and cure depth utilizing different resin-based materials, initiators, and irradiation intensities for given doses to evaluate the validity of the reciprocity law for filled and unfilled systems. Musanje and Darvell evaluated a series of commercial composites and found that different doses were required to achieve complete material properties for different irradiation intensities. Peutzfeld and Asmussen determined that degree of cure decreased with increased irradiation intensity for equivalent doses . In these studies, as well as others , the results and observed correlations regarding reciprocity varied depending on the type of material, the curing parameters that were utilized, and the degree of cure that was achieved during irradiation.

Inherently, as noted, the reciprocity law implies a scaling between the rate or extent of a process and its dependence on light intensity. Generally, for a given photoinitiated process, the overall rate of change of a particular species concentration in that process broadly can be assumed to scale with light intensity. Thus, for a particular species, Z, with a concentration [Z], the rate of reaction for that species, R _Z is a function of its own concentration, the temperature, T , the concentration of other species in the reaction (broadly represented by [N]) and the light intensity, LI , as follows:

Here, f () represents an arbitrary function that describes the process that is occurring and a represents an exponent indicating the functional scaling of the targeted rate on light intensity. For a = 1, the process would be linear and the rate of the reaction would be proportional to the light intensity. When a = 1 and the function f is a constant over time, then Eq. (1) above can be integrated to find

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