Fotogametri Dijital• Pertemuan ke - 2

Pokok Bahasan: Pengenalan konsep Akusisi Data Foto digital

Sub Pokok Bahasan:1. Sistem Lensa kamera dijital2. Prinsip kamera lubang jarum – Teori perspektif3. Finite Field of View, Depth of Field4. Distorsi Lensa: Abrasi dan geometrik

Susunan Lensa• Fungsi Utama – Mengumpulkan berkas sinar yang

dipantulkan obyek dan memfokuskan berkas sinar kebidang ke bidang sensor:– Menggunakn prinsip refraksi– f : focal length (panjang fokus)– F : focal point of lens (titik fokus lensa)

• Optical axis (Sumbu Optik):– Garis penghubung antar titik fokus lensa

Susunan Lensa

Kamera Lubang Jarum (Pinhole camera)

"When images of illuminated objects ... penetrate through a small hole into a very dark room ... you will see [on the opposite wall] these objects in their proper form and color, reduced in size ... in a reversed position, owing to the intersection of the rays". Da Vinci (Russell

Naughton , http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html )

Model Kamera Lubang Jarum (2D)• Model kamera lubang jarum menggambarkan proses geometrik pencitraan/

pemotretan suatu obyek pada bidang fokus/ sensor (image plane)• Gambar / foto yang terbentuk akan terbalik (atas ke bawah)

Gambar obyek akan terlihat terbalik pada bidang

sensor (image plane).X’ = (f’ / Z) X

Karakteristik Geometrik Kamera Lubang Jarum

Dimensi obyek berbanding terbalik dengan jaraknya ke kamera

(Gambar kiri).

Obyek yang lebih jauh akan terlihat lebih kecil (Gambar kiri).

Garis akan diproyeksikan sebagai garis. Dua garis yang sejajar (paralel)

akan bertemu di titik “vanishing point”(VP) (Gambar kanan).

Setiap VP dari pasangan garis sejajar akan membentuk sebuah garis

lurus (Horizon H)

Sudut difoto dengan obyeknya berbeda.

Weak perspective (affine projection)

Assume object points are all at same depth -z0

Orthographic projection

Perspective models photos(Strong Perspective)

• Angles are not preserved

• The projections of parallel lines intersect at one point

Perspective models photos

Perspective models photos

Pinhole Model: (Strong) Camera Projection

Geometric model of camera projection

– Image plane I, which rays intersect

– Camera center C, through which all rays pass

– Focal length f, distance from I to C

Point (X,Y,Z) in space and image (x,y) in I – Simplified case

C at origin in space

I perpendicular to Z axis

x=fX/Z (x/f=X/Z) y=fY/Z (y/f=Y/Z) Projective Geometry/transformation

Problems with Pinholes

• Pinhole size (aperture) must be “very small” to obtain a clear image.

• However, as pinhole size is made smaller, less light is received by image plane.

• If pinhole is comparable to wavelength of incoming light, DIFFRACTION blurs the image!

• Sharpest image is obtained when: pinhole diameter Example: If f’ = 50mm,

= 600nm (red), d = 0.36mm

'.2 fd

The reason for lenses

Thin lenses model (paraxial optics)

Pinhole model with a single lens

A lens follows the pinhole model for objects that are in focus.

An out-of-focus lens

An image plane at the wrong distance means that rays from

different parts of the lens create a blurred region (the “point

spread function”).

Depth of field is smaller for small f-number

Finite Field of View

Finite Aperture

Depth of Field

Range of object distances over which image is sufficiently well focused.

Range for which blur circle is less than the resolution of the sensor

Without introducing significant image deterioration

Can be increased by reducing aperture

Shorter focal length –greater depth of field

Resolution (resolving power): Ability of lens to show detail Line pairs or modulation transfer function Good resolution important Sharp & clear for precise measurements & accurate

interpretative work

Real Lenses Systems

• The best modern lenses may contain

aspherical aberration

Spherical aberrations

• Rays further from the optical axis are focused closer to the lens• Aberrations:

– Degrades sharpness of image– Blurs image– Caused by faulty grinding of the lens

Geometric or Lens Distortions

• One of many sources of geometric distortion is Aberrations

• Lens distortion:– Degrades geometric quality (positional accuracy)

– Symmetric radial – distorts along radial lines from optical axis• Caused by faulty grinding of lens

• Outward +, inward –

– Decentering – tangential & asymmetric radial components• Causes off-center distortion pattern

• Caused by faulty alignment of individual lens elements

Geometric or Lens distortions