Exploring the Relationship Between Optical Density, Absorbance, and Transmittance in Spectrophotometry

Spectrophotometric-based assays are indispensable tools in scientific research, offering swift and precise quantification in various scientific disciplines. Understanding how light interacts with a sample unveils crucial information about its properties, including concentration. Let’s dive deep into some crucial facts frequently encountered when performing such assays: optical density (OD), absorbance, and transmittance. 

What is Optical Density?

Optical density (OD) measures the attenuation of light intensity as it passes through a medium. In practical terms, it measures the amount of light taken up by the solution. It is a logarithmic quantity that describes the reciprocal of transmittance (T), which is the ratio of the intensity of light transmitted through a material (I) to the intensity of the incident light (I₀).

OD formula: OD = - Log₁₀(T) = Log₁₀ (I₀ / I) 

Imagine firing a light beam with 100 photons at a substance (Fig. 1). As the light travels, some photons get absorbed by the substance, while others get scattered in different directions (think of them bouncing around like billiard balls). If only 10 of the original 100 photons manage to pass through and emerge on the other side, then the OD would be:     

OD = Log₁₀10 (100/10) = 1

An OD of 0 indicates that all the light is transmitted, while an OD of infinity indicates that all the light is absorbed. OD is influenced by both absorbance and scattering, which contribute to the OD value. 

What is Light Absorbance? 

Absorbance refers to the amount of light a substance absorbs at a particular wavelength. It measures the interaction between light and the material's ability to absorb that specific light energy (Fig. 2). Higher absorbance indicates stronger absorption.    

For example, techniques like the BCA assay allow scientists to estimate the total amount of protein in a solution by measuring the absorbance at a specific wavelength. The higher the absorbance, the more protein is likely present.  

What is Light Scattering?

Light scattering occurs when light deviates from its path due to interactions with particles or irregularities within a medium (Fig. 2). This scattering can affect the optical density measurement by influencing the amount of light scattered or transmitted by the sample.    

In practical applications, light scattering is utilized, for instance, in turbidity measurements, to determine bacterial concentration or growth. When light passes through a solution containing bacteria, bacteria cause light to scatter in various directions. This contributes to the overall reduction in transmitted light and influences OD measurement. So, an increase in bacterial concentration (more scatterers) will lead to a higher OD value.    

Before we move into further details, it is essential to note that optical density (OD) accounts for both light absorption and scattering. However, OD is often used interchangeably with absorbance in practical applications, mainly when light scattering is minimal or consistent.  

Connection: Transmittance to Absorbance

Transmittance (T) is the fraction of light that passes through a sample compared to the initial light intensity. It is a measure of how much light gets transmitted. Transmittance is calculated as T = I /  I₀. Transmittance can also be expressed as a percentage T (%) = (I /  I₀) x 100 

where:

• T is transmittance (unitless)
• I is the intensity of light transmitted through the sample
• I₀ is the intensity of the incident light   

Transmittance ranges from 0 to 1, where:

• T = 1 indicates all the light passed through, and the sample is entirely transparent.  
• T = 0 indicates none of the light got through, and the sample completely absorbed the light.  

Absorbance (A), on the other hand, tells you how much light the sample absorbs. It's the flip side of transmittance. Absorbance is calculated using the logarithm of the reciprocal of transmittance:  A = Log₁₀(1/ T) = Log₁₀ (I₀ / I) 

There's an inverse relationship between absorbance and transmittance. As the amount of light absorbed (A) increases, the amount of light transmitted (T) decreases, and vice versa.  Thus, 

• A = 0 indicates that 100% of light has been transmitted through the sample  
• A = 1 indicates 10% of the light has been transmitted through the sample  
• A = 2 indicates 1% of the light has been transmitted through the sample   

How does a spectrophotometer measure absorbance? 

The next question arises: How can we apply a spectrophotometer to measure absorbance? Let's simplify the process into easy-to-understand steps:  

• The spectrophotometer emits light of various wavelengths. Typically, this light source covers multiple various wavelengths, such as ultraviolet (UV), visible, and near-infrared (NIR) regions.
• The emitted light passes through a monochromator or a filter-based system. In both cases, the system selects a specific wavelength of light, ensuring that only light of the desired wavelength reaches the sample. For example, for OD600 bacterial measurement, only a wavelength of 600 nm passes the sample.
• The selected wavelength of light then passes through the sample compartment, where the substance being analyzed is placed.  

• On the other side of the sample compartment, there's a detector that measures the amount of light transmitted through the sample and the light absorbed.  
• The light energy transmitted through the substance is measured on the spectrophotometer by comparing the reference/incident light intensity (I0) and the transmitted light intensity(I). The value of absorbance can be then also calculated.   

Meet Absorbance One 

Shedding light on Beer-Lambert Law: Connecting Absorbance and Concentration

Now that we've covered absorbance and transmittance, you might wonder why these concepts matter. They are essential because they enable us to measure the concentration of a sample using Beer-Lambert's Law. Let’s dive deep into some fundamentals of calculating or finding concentration from absorbance.

The Beer-Lambert Law is the fundamental principle that describes the relationship between light absorption and the properties of the substance (Fig. 3). It states that the light absorbed can be directly proportional to the concentration of the sample and the path length of the light through the solution:     

A = εlc  

Where,    

• A is the absorbance (dimensionless)  
• ε is the molar absorptivity coefficient (M⁻¹cm⁻¹)  
• l is the path length of the light through the solution (cm)  
• c is the concentration of the absorbing sample (M)    

Absorbance, therefore, exhibits a linear relationship with concentration according to Beer-Lambert Law.

Beer's Law Limits: When Absorbance Doesn't Reflect Concentration Linearly    

Beer's Law is a fantastic tool for estimating concentration based on absorbance, but there is a catch: it only holds under specific conditions. At high concentrations, the sample molecules get packed closer together. This can lead to stronger interactions between them and light scattering, which can alter how they absorb light. Beer's Law assumes a simple proportional relationship, and these interactions at high concentrations disrupt that linearity (Fig. 4). 

Thus, the relationship between absorbance and concentration deviates from the nice straight line predicted by Beer's Law in such situations; so, if you use Beer's Law on a sample that's too concentrated, you'll likely get an inaccurate estimate of the actual concentration. 

Conclusion  

Understanding the interplay between OD, absorbance, and transmittance is crucial for accurate spectrophotometric measurements. Mastering these concepts can enhance the precision of your experiments and confidently interpret your data. Keep these principles in mind to ensure reliable and reproducible results in your research.