For long wavelength gravitational wave (GW), it is easy to diffract when it

is lensed by celestial objects. Traditional diffractive integral formula has

ignored large angle diffraction, which is adopted in most of cases. However, in

some special cases (e. g. a GW source lensed by its companion in a binary

system, where the lens is very close to the source), large angle diffraction

could be important. Our previous works have proposed a new general diffractive

integral formula which has including large angle diffraction case. In this

paper, we have investigated how much difference between this general

diffractive formula and traditional diffractive integral formula could be under

these special cases with different parameters. We find that the module of

amplification factor for general diffractive formula could become smaller than

that of traditional diffractive integral basically with a factor

$r_Fsimeq0.674$ when the distance between lens and sources is $D_{rm LS}=1$

AU and lens mass $M_{rm L}=1M_odot$. Their difference is so significant that

it is detectable. Furthermore, we find that the proportionality factor $r_F$ is

gradually increasing from 0.5 to 1 with increasing $D_{rm LS}$ and it is

decreasing with increasing $M_{rm L}$. As long as $D_{rm LS}lesssim3$ AU

(with $M_{rm L}=1M_odot$) or $M_{rm L}gtrsim0.1M_odot$ (with $D_{rm

LS}=1$ AU ), the difference between new and traditional formulas is enough

significant to be detectable. It is promising to test this new general

diffractive formula by next-generation GW detectors in the future GW detection.

## The Future of Gravitational Wave Detection: Challenges and Opportunities

Gravitational waves (GW) have revolutionized our understanding of the universe, providing new insights into the nature of space-time and the objects that inhabit it. However, the detection and analysis of GW signals are complex tasks that require advanced mathematical formulas and sophisticated instruments. In this article, we will explore a new general diffractive integral formula for GW detection and discuss its potential impact on future observations.

### The Importance of Large Angle Diffraction

In most cases, traditional diffractive integral formulas have ignored large angle diffraction when it comes to long wavelength GW lensed by celestial objects. However, recent research has shown that in some special cases, such as a GW source being lensed by its companion in a binary system with a close lens-source distance, large angle diffraction plays a crucial role.

### The New General Diffractive Integral Formula

Previous works have proposed a new general diffractive integral formula that takes into account large angle diffraction. This formula offers a more comprehensive approach to GW detection and has the potential to reveal crucial information about the nature of gravitational waves.

### Investigating the Difference

In this study, the researchers compared the general diffractive formula with the traditional diffractive integral formula under different parameters. They found that the module of amplification factor for the general formula is smaller than that of the traditional formula by a factor of approximately $r_Fsimeq0.674$, when the lens-source distance is $D_{rm LS}=1$ AU and the lens mass is $M_{rm L}=1M_odot$. This difference is significant enough to be detectable.

### Potential Challenges

While the new general diffractive formula shows promising results, there are some challenges that need to be addressed in future research and observations. One challenge is the optimization of GW detectors to accurately measure the difference between the two formulas. This may require advancements in detector sensitivity and calibration techniques.

### Opportunities for Future GW Detection

The researchers also found that the proportionality factor $r_F$ gradually increases from 0.5 to 1 with increasing lens-source distance ($D_{rm LS}$), and decreases with increasing lens mass ($M_{rm L}$). This finding suggests that the difference between the new and traditional formulas remains detectable as long as $D_{rm LS}lesssim3$ AU (with $M_{rm L}=1M_odot$) or $M_{rm L}gtrsim0.1M_odot$ (with $D_{rm LS}=1$ AU). These results highlight the potential of next-generation GW detectors to test and validate the new general diffractive formula.

### The Roadmap Ahead

With the advancements in GW detection technology and the introduction of the new general diffractive integral formula, the future of gravitational wave research looks promising. Scientists and engineers need to focus on optimizing detector sensitivity, improving calibration techniques, and conducting extensive observations to validate the results obtained from the new formula. By doing so, we can further our understanding of gravitational waves and unlock the mysteries of the universe.

Disclaimer:The information provided in this article is based on current research findings and is subject to change as new data becomes available. Readers are encouraged to stay updated with the latest advancements in the field.