Optics

1. Theoretical Concepts in Optics
   1. Fourier Optics
      1. Fourier transforms in optics
         1. Definition and mathematical formulations
         2. Application to optical systems
      2. Optical transfer functions
         1. Concepts of frequency components and system response
      3. Spatial filtering
         1. Basics of spatial filtering and its implications
         2. Use of optical filters in modifying transfer functions
      4. Applications of Fourier optics
         1. Image processing
         2. Pattern recognition
         3. Holography
   2. Optical Coherence Theory
      1. Concept of coherence
         1. Temporal coherence
            1. Definition and measurement
            2. Role in interference phenomena
         2. Spatial coherence
            1. Definition and practical implications
            2. Coherence length and its determination
      2. Coherence in optical systems
         1. Importance for imaging and laser systems
      3. Applications of coherence
         1. Interferometric techniques
         2. Coherence tomography and imaging
   3. Holography
      1. Basic principles of holography
         1. Recording and reconstructing light wavefronts
         2. Difference between photographs and holograms
      2. Types of holography
         1. Transmission holography
            1. Recording process and viewing conditions
         2. Reflection holography
            1. Characteristics and applications
         3. Denisyuk holography
            1. Specifics and unique properties
      3. Techniques in holography
         1. Holographic recording mediums
            1. Photographic plates
            2. Photopolymers and other modern materials
         2. Digital holography
            1. Methods and advancements
      4. Applications of holography
         1. Data storage
         2. Art and display purposes
         3. Microscopy and metrology
   4. Mathematical Modeling in Optics
      1. Rayleigh-Sommerfeld diffraction theory
         1. Mathematical models for light propagation
         2. Applications and limitations
      2. Fresnel-Kirchhoff diffraction formula
         1. Derivation and significance
         2. Use cases in optics
      3. Mie theory and scattering
         1. Principles and applications in particle scattering
   5. Advanced Theoretical Techniques
      1. Numerical methods in optics
         1. Finite Difference Time Domain (FDTD) method
            1. Basics and applications
         2. Beam Propagation Method (BPM)
            1. Simulation techniques in waveguide analysis
      2. Computational models in light propagation
         1. Software tools for simulation
         2. Real-world applications and challenges
   6. Theoretical Developments and Challenges
      1. Quantum optical theory advances
         1. Integrating classical and quantum approaches
         2. Impact on technologies like lasers and quantum computing
      2. Expanding the limits of wave optics
         1. Overcoming classical constraints
         2. Emerging areas such as metamaterials and nano-optics